[ambrosio]

Full Professor, SNS Pisa

**Email:** *ambrosio AT sns.it*

- L. Ambrosio - S. Honda - D. Tewodrose (Submitted Paper)

Short-time behavior of the heat kernel and Weyl's law on $RCD^*(K,N)$ spaces (2017) - L. Ambrosio - S. Honda (Submitted Paper)

Local spectral convergence in $RCD^*(K,N)$ spaces (2017) - L. Ambrosio (Submitted Paper)

Well posedness of ODE's and continuity equations with nonsmooth vector fields, and applications (2017) - L. Ambrosio - F. Stra - D. Trevisan (Submitted Paper)

Weak and strong convergence of derivations and stability of flows with respect to MGH convergence (2016) - L. Ambrosio - S. Honda (Submitted Paper)

New stability results for sequences of metric measure spaces with uniform Ricci bounds from below (2016) - L. Ambrosio - D. Puglisi (Submitted Paper)

Linear extension operators between spaces of Lipschitz maps and Optimal Transport} (2016) - L. Ambrosio - A. Mondino (
*Rend. Lincei Mat. Appl.*)

Gaussian-type Isoperimetric Inequalities in $RCD(K,\infty)$ probability spaces for positive $K$ (2016) - L. Ambrosio - G. E. Comi (Submitted Paper)

Anisotropic surface measures as limits of volume fractions (2016) - L. Ambrosio - F. Stra - D. Trevisan (Preprint)

A PDE approach to a 2-dimensional matching problem (2016) - L. Ambrosio - S. Di Marino - N. Gigli (Submitted Paper:
*Nonlinear Analysis: Theory, Methods & Applications*)

Perimeter as relaxed Minkowski content in metric measure spaces (2016) - L. Ambrosio (Submitted Paper)

Regularity theory for mass-minimizing currents (after Almgren-De Lellis-Spadaro) (2015) - L. Ambrosio - H. Brezis - J. Bourgain - A. Figalli (Accepted Paper:
*Comm. Pure Appl. Math.*)

$BMO$-type norms related to the perimeter of sets (2015) - L. Ambrosio - J. Bertrand (Submitted Paper)

DC Calculus (2015) - L. Ambrosio - D. Trevisan (Preprint)

Lecture notes on the DiPerna-Lions theory in abstract measure spaces (2015) - L. Ambrosio - C. De Lellis - T. Schmidt (
*J. Reine Angew. Math.*)

Partial regularity for mass-minimizing currents in Hilbert spaces (2015) - L. Ambrosio - M. Colombo - A. Figalli (Accepted Paper:
*Arch. Ration. Mech. Anal.*)

Existence and uniqueness of maximal regular flows for non-smooth vector fields (2015) - L. Ambrosio - M. Erbar - G. Savaré (Submitted Paper)

Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces (2015) - L. Ambrosio - M. Miranda Jr - D. Pallara (Accepted Paper:
*Anal. Geom. Metr. Spaces*)

Some fine properties of $BV$ functions on Wiener spaces (2015) - L. Ambrosio - R. Ghezzi (Submitted Paper)

Sobolev and Bounded Variation Functions on Metric Measure Spaces (2015) - L. Ambrosio - R. Ghezzi - V. Magnani (
*Ann. Inst. H. Poincaré Anal. Non Linéaire*)

BV functions and sets of finite perimeters in sub-Riemannian manifolds (2015) - L. Ambrosio - A. Pinamonti - G. Speight (Accepted paper:
*J. Reine Angew. Math.*)

Weighted Sobolev spaces on metric measure spaces (2015) - L. Ambrosio - A. Mondino - G. Savaré (Accepted Paper:
*Memoirs Amer. Math. Soc.*)

Nonlinear diffusion equations and curvature conditions in metric measure spaces (2015) - L. Ambrosio - S. Di Marino (
*J. Funct. Anal.*)

Equivalent definitions of $BV$ space and of total variation on metric measure spaces (2014) - L. Ambrosio - D. Trevisan (
*Analysis and PDE*)

Well posedness of Lagrangian flows and continuity equations in metric measure spaces (2014) - L. Ambrosio - A. Mondino - G. Savaré (Accepted Paper:
*Journal of Geometric Analysis*)

On the Bakry-Èmery condition, the gradient estimates and the Local-to-Global property of $RCD^*(K,N)$ metric measure spaces (2014) - L. Ambrosio - G. Crippa (
*Proceedings of the Royal Society of Edinburgh: Section A*)

Continuity equations and ODE flows with non-smooth velocity (2014) - L. Ambrosio - A. Pinamonti - G. Speight (Accepted Paper:
*Advances in Mathematics*)

Tensorization of Cheeger energies, the space $H^{1,1}$ and the area formula for graphs (2014) - L. Ambrosio - M. Colombo - A. Figalli (Submitted Paper)

On the Lagrangian structure of transport equations: the Vlasov-Poisson system (2014) - L. Ambrosio - T. Schmidt (
*Proc. Lond. Math. Soc. (3)*)

Compactness results for normal currents and the Plateau problem in dual Banach spaces (2013) - L. Ambrosio - J. Feng (Submitted Paper)

On a class of first order Hamilton-Jacobi equations in metric spaces (2013) - L. Ambrosio - S. Di Marino - G. Savaré (Submitted Paper)

On the duality between $p$-modulus and probability measures (2013) - L. Ambrosio - T. Rajala (Accepted Paper:
*Ann. Mat. Pura Appl.*)

Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces (2012) - L. Ambrosio - M. Colombo - G. De Philippis - A. Figalli (Accepted Paper:
*Comm. Partial Differential Equations*)

Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case (2012) - L. Ambrosio - N. Gigli - G. Savaré (Preprint)

Heat flow and calculus on metric measure spaces with Ricci curvature bounded below - the compact case (2012) - L. Ambrosio - G. Crasta - V. De Cicco - G. De Philippis (Accepted Paper:
*Manuscripta Math.*)

A nonautonomous chain rule in $W^{1,1}$ and in $BV$ (2012) - L. Ambrosio - F. Ghiraldin (
*Ann. Inst. H. Poincaré Anal. Non Linéaire*)

Flat chains with finite size in metric spaces (2012) - L. Ambrosio - F. Ghiraldin (
*Analysis and Geometry in Metric Spaces*)

Compactness of special functions of bounded higher variation (2012) - L. Ambrosio - M. Colombo - G. De Philippis - A. Figalli (Accepted Paper:
*Discrete Contin. Dyn. Syst.*)

A global existence result for the semigeostrophic equations in three dimensional convex domains (2012) - L. Ambrosio - A. Figalli - E. Runa (Accepted Paper:
*Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl.*)

On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces (2012) - L. Ambrosio - N. Gigli - A. Mondino - T. Rajala (Accepted Paper:
*Transactions of the AMS*)

Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure (2012) - L. Ambrosio - N. Gigli - G. Savaré (Submitted Paper)

Bakry-Emery curvature-dimension condition and Riemannian Ricci curvature bounds (2012) - L. Ambrosio - G. Da Prato - B. Goldys - D. Pallara (
*Comm. P. D. E.*)

Bounded variation with respect to a log-concave measure (2012) - L. Ambrosio - M. Colombo - S. Di Marino (Accepted Paper:
*Advanced Studies in Pure Mathematics: "Variational methods for evolving objects"*)

Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope (2012) - L. Ambrosio - N. Gigli

A user's guide to optimal transport (2011) - L. Ambrosio - A. Figalli - G. Friesecke - J. Giannoulis - T. Paul (Accepted Paper:
*Comm. Pure Appl. Math.*)

Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data (2011) - L. Ambrosio - G. De Philippis - L. Martinazzi (
*Manuscripta Math.*)

Gamma-convergence of nonlocal perimeter functionals (2011) - L. Ambrosio - G. De Philippis - B. Kirchheim (
*Rend. Lincei - Mat. e Appl.*)

Regularity of optimal transport maps and partial differential inclusions (2011) - L. Ambrosio (Proceedings)

An overview on calculus and heat flow in metric measure spaces and spaces with Riemannian curvature bounded from below (2011) - L. Ambrosio - E. Mainini - S. Serfaty (
*Ann. Inst. H. Poincaré Anal. Non Linéaire*)

Gradient flow of the Chapman-Rubinstein-Schatzman model for signed vortices (2011) - L. Ambrosio - N. Gigli - G. Savaré (Submitted Paper)

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below (2011) - L. Ambrosio - N. Gigli - G. Savaré (Submitted Paper)

Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces (2011) - L. Ambrosio - N. Gigli - G. Savaré (Submitted Paper)

Metric measure spaces with Riemannian Ricci curvature bounded from below (2011) - L. Ambrosio - S. Maniglia - M. Miranda Jr - D. Pallara (
*J. Funct. Anal.*)

BV functions in abstract Wiener spaces (2010) - L. Ambrosio - S. Maniglia - M. Miranda Jr - D. Pallara (
*Physica D*)

Towards a theory of BV functions in abstract Wiener spaces (2010) - L. Ambrosio - G. Crippa - A. Figalli - L. V. Spinolo (Proceedings:
*IMA Vol. Math. Appl., Springer*)

Existence and uniqueness results for the continuity equation and applications to the chromatography system (2010) - L. Ambrosio - A. Figalli (Accepted Paper:
*Ann. Fac. Sci. Toulouse Math.*)

Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces (2010) - L. Ambrosio - G. Da Prato - D. Pallara (
*Rend. Acc. Lincei*)

BV functions in a Hilbert space with respect to a Gaussian measure (2010) - L. Ambrosio - E. Durand-Cartagena (Preprint)

Stepanov's Theorem in Wiener spaces (2010) - L. Ambrosio - A. Figalli (Accepted Paper:
*C. R. Math. Acad. Sci. Paris*)

Almost everywhere well-posedness of continuity equations with measure initial data (2010) - L. Ambrosio - A. Carlotto - A. Massaccesi

Lecture Notes on Partial Differential Equations (2010) - L. Ambrosio - E. Mainini (
*J. Evol. Equ.*)

Infinite-dimensional porous media equations and optimal transportation (2010) - L. Ambrosio - M. Miranda Jr - D. Pallara (
*Discrete Contin. Dyn. Sys.*)

Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability (2010) - L. Ambrosio - A. Lemenant - G. Royer-carfagni (
*Journal of Elasticity*)

A variational model for plastic slip and its regularization via Gamma-convergence. (2010) - L. Ambrosio - E. Durand-Cartagena (
*Rend. Circ. Mat. Palermo*)

Metric differentiability of Lipschitz maps defined on Wiener spaces (2009) - L. Ambrosio - G. Crippa - A. Figalli - L. V. Spinolo (
*SIAM J. Math. Anal.*)

Some new well-posedness results for continuity and transport equations, and applications to the chromatography system (2009) - L. Ambrosio - M. Scienza (Submitted Paper)

Locality of the perimeter in Carnot groups and chain rule (2009) - L. Ambrosio - A. Figalli (Lecture notes)

Lecture notes on variational models for incompressible Euler equations (2009) - L. Ambrosio - M. Katz (Submitted Paper)

Flat currents modulo $p$ in metric spaces and filling radius inequalities (2009) - L. Ambrosio (Submitted Paper)

The flow associated to weakly differentiable vector fields: recent results and open problems (2009) - L. Ambrosio - G. Friesecke - J. Giannoulis (Submitted Paper)

Passage from quantum to classical molecular dynamics in the presence of Coulomb interactions (2009) - L. Ambrosio - S. Wenger (Submitted Paper)

Rectifiability of flat chains in Banach spaces with coefficients in $*Z*_p$ (2009) - L. Ambrosio - B. Kleiner - E. Le Donne (Preprint)

Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane (2008) - L. Ambrosio - G. Crippa - P. G. LeFloch (
*Netw. Heterog. Media*)

Leaf superposition property for integer rectifiable currents (2008) - L. Ambrosio - H. Frid - J. Silva (Accepted Paper:
*Journal of Functional Analysis*)

Multiscale Young Measures in Homogenization of Continuous Stationary Processes in Compact Spaces and Applications (2008) - L. Ambrosio - G. Crippa (
*In: Transport Equations and Multi-D Hyperbolic Conservation Laws, Lecture Notes of the Unione Matematica Italiana*)

Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields (2008) - L. Ambrosio - N. Gigli (Accepted Paper:
*Methods and Applications of Analysis*)

Construction of the parallel transport in the Wasserstein space (2008) - L. Ambrosio - P. Bernard (Submitted Paper)

Uniqueness of signed measures solving the continuity equation for Osgood vector fields (2008) - L. Ambrosio - A. Figalli (Accepted Paper:
*J. Funct. Anal.*)

On flows associated to Sobolev vector fields in Wiener spaces: an approach a' la DiPerna-Lions (2008) - L. Ambrosio - F. Santambrogio (
*Rend. Lincei - Mat. e Appl.*)

Necessary optimality conditions for geodesics in weighted Wasserstein spaces (2007) - L. Ambrosio - G. Savare' - L. Zambotti (Accepted Paper:
*Probability Theory and Related Fields*)

Existence and Stability for Fokker-Planck equations with log-concave reference measures (2007) - L. Ambrosio - A. Figalli (Accepted Paper:
*Calc. Var. Partial Differential Equations*)

On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations (2007) - L. Ambrosio - A. Colesanti - E. Villa (Submitted Paper)

One-sided Minkowski content for some classes of closed sets and applications to stochastic geometry (2007) - L. Ambrosio - S. Serfaty (Submitted Paper)

A gradient flow approach to an evolution problem arising in superconductivity (2007) - L. Ambrosio - A. Figalli (Accepted Paper:
*Arch. Rat. Mech. Anal.*)

Geodesics in the space of measure-preserving maps and plans (2007) - L. Ambrosio - C. De Lellis - J. Malý (
*Perspective in nonlinear partial differential equations*)

On the chain rule for the divergence of BV like vector fields: applications, partial results, open problems (2007) - L. Ambrosio - V. Capasso - E. Villa (Submitted Paper)

On the approximation of geometric densities of random closed sets (2006) - L. Ambrosio - S. Lisini - G. Savare' (
*manuscripta math.*)

Stability of flows associated to gradient vector fields and convergence of iterated transport maps (2006) - L. Ambrosio - F. Serra Cassano - D. Vittone (
*J. Geom. Anal.*)

Intrinsic regular hypersurfaces in Heisenberg groups (2006) - L. Ambrosio - J. Malý (Submitted Paper)

Very weak notions of differentiability (2005) - L. Ambrosio - G. Crippa - S. Maniglia (
*Ann. Fac. Sci. Toulouse Math. (6)*)

Traces and fine properties of a $BD$ class of vector fields and applications (2005) - L. Ambrosio (Accepted Paper)

Steepest descent flows and applications to spaces of probability measures (2005) - L. Ambrosio - H. Frid (Submitted Paper)

Multiscale Young measures in almost periodic homogenization and applications (2005) - L. Ambrosio - M. Lecumberry - S. Maniglia (Submitted Paper)

Lipschitz regularity and approximate differentiability of the DiPerna-Lions flow (2005) - L. Ambrosio (Preprint)

Transport equation and Cauchy problem for non-smooth vector fields (2005) - L. Ambrosio - W. Gangbo (Submitted Paper)

Hamiltonian ODE's in the Wasserstein space of probability measures (2005) - L. Ambrosio - F. Bouchut - C. De Lellis (
*Comm. Partial Differential Equations*)

Well--posedness for a class of hyperbolic systems of conservation laws in several space dimensions (2004) - L. Ambrosio - B. Kirchheim - A. Pratelli (
*Duke Math. J.*)

Existence of optimal transport maps for crystalline norms (2004) - L. Ambrosio - M. Miranda Jr - D. Pallara (
*Quad. Mat.*)

Special Functions of Bounded Variation in Doubling Metric Measure Spaces (2004) - L. Ambrosio - C. De Lellis (
*J. Hyperbolic Diff. Equ.*)

A note on admissible solutions of 1d scalar conservation laws and 2d Hamilton-Jacobi equations (2004) - L. Ambrosio (Lecture Notes)

Lecture notes on transport equation and Cauchy problem for $BV$ vector fields and applications (2004) - L. Ambrosio (Accepted Paper:
*Inventiones Mathematicae*)

Transport equation and Cauchy problem for BV vector fields (2003) - L. Ambrosio - C. De Lellis (
*International Mathematics Research Notices*)

Existence of solutions for a class of hyperbolic systems of conservation laws in several space dimensions (2003) - L. Ambrosio - N. Gigli - G. Savare' (Accepted Paper)

Gradient flows with metric and differentiable structures, and applications to the Wasserstein space (2003) - L. Ambrosio - V. Magnani (
*Math. Z.*)

Weak differentiability of BV functions on stratified groups (2003) - L. Ambrosio - M. Lecumberry - T. Riviere (Accepted Paper:
*Communications on Pure and Applied Mathematics*)

A viscosity property of minimizing micromagnetic configurations (2002) - L. Ambrosio - B. Kirchheim - M. Lecumberry - T. Riviere

On the rectifiability of defect measures arising in a micromagnetics model (2002) - L. Ambrosio - S. Masnou (Accepted Paper:
*Interfaces and Free Boundaries*)

A direct variational approach to a problem arising in image reconstruction (2002) - L. Ambrosio (
*Set Valued Analysis*)

Fine properties of sets of finite perimeter in doubling metric measure spaces (2002) - L. Ambrosio - M. Novaga - E. Paolini (
*ESAIM: COCV volume dedicated to J. L. Lions*)

Some Regularity Results for Minimal Crystals (2002) - L. Ambrosio - S. Rigot (Accepted Paper:
*Journal of Functional Analysis*)

Optimal Mass Transportation in the Heisenberg Group (2002) - L. Ambrosio - A. Pratelli

Existence and stability results in the $L^1$ theory of optimal transportation (2002) - L. Ambrosio (
*Advances in Mathematics*)

Some Fine Properties of Sets of Finite Perimeter in Ahlfors Regular Metric Measure Spaces (2001) - L. Ambrosio - V. Caselles - S. Masnou - J. M. Morel (
*Journal of EMS.*)

Connected Components of Sets of Finite Perimeter and Applications to Image Processing (2001) - L. Ambrosio - L. Faina - R. March (
*SIAM J. Math. Anal.*)

Variational Approximation of a Second Order Free Discontinuity Problem in Computer Vision (2001) - L. Ambrosio - P. Colli Franzone - G. Savaré (
*Interfaces and Free Boundaries*)

Gamma-Convergence of a Family of Anisotropic Functionals with Lack of Coercivity (2000) - L. Ambrosio (Lecture Notes)

Lecture Notes on Optimal Transport Problems (2000) - G. Alberti - L. Ambrosio - X. Cabrè (
*Acta Appl. Math.*)

On a long standing conjecture of E. De Giorgi: old and recent results (2000) - L. Ambrosio - X. Cabrè (
*Journal of the AMS*)

Entire Solutions of a Semilinear Elliptic Equation in ${\mathcal R}^3$ and a Conjecture of De Giorgi (2000) - L. Ambrosio - B. Kirchheim (
*Acta Mathematica*)

Currents in Metric Spaces (2000) - L. Ambrosio - N. Fusco - D. Pallara (
*Diff. Int. Eqs.*)

Higher Regularity of Solutions of Free Discontinuity Problems (1999) - L. Ambrosio - E. Paolini (
*Ricerche di Matematica*)

Partial regularity for quasi minimizers of perimeter (1999) - L. Ambrosio - B. Kirchheim (
*Submitted to Math. Annalen.*)

Rectifiable Sets in Metric and Banach Spaces (1999) - L. Ambrosio - C. De Lellis - C. Mantegazza (
*Calc. Var.*)

Line Energies for Gradient Vector Fields in the Plane (1999) - L. Ambrosio - I. Fonseca - P. Marcellini - L. Tartar (
*To appear on Arch. Rat. Mech. Anal.*)

On a Volume Constrained Variational Problem (1998) - L. Ambrosio - C. Mantegazza (
*J. Geom. Anal.*)

Curvature and Distance Function from a Manifold (1998) - L. Ambrosio - M. Gobbino - D. Pallara (
*J. Geom. Anal.*)

Approximation problems for curvature varifolds (1998) - L. Ambrosio - A. Coscia - G. Dal Maso (
*Arch. Rational Mech. Anal.*)

Fine Properties of Functions with Bounded Deformation (1997) - L. Ambrosio - D. Pallara (
*Annali della Scuola Normale Superiore di Pisa*)

Partial Regularity of Free Discontinuity Sets I (1997) - L. Ambrosio - N. Fusco - D. Pallara (
*Annali della Scuola Normale Superiore di Pisa*)

Partial Regularity of Free Discontinuity Sets II (1997) - L. Ambrosio - A. Braides (Paper in Volume:
*Homogenization and Applications to Material Sciences, (D. Cioranescu, A. Damlamian, P. Donato eds.) GAKUTO, Gakkotosho, Tokio, Japan*)

Energies in SBV and variational models in fracture mechanics. (1997) - G. Alberti - L. Ambrosio (
*Math. Zeit.*)

A Geometrical Approach to Monotone Functions in ${\mathbb R}^n$ (1996) - L. Ambrosio - A. Braides - A. Garroni (partially unpublished manuscript)

Special functions with bounded variation and with weakly differentiable traces on the jump set (1995) - L. Ambrosio - A. Braides (
*J. Math. Pures. Appl.*)

Functionals defined on partitions of sets of finite perimeter, I: integral representation and $\Gamma$-convergence (1990) - L. Ambrosio - A. Braides (
*J. Math. Pures. Appl.*)

Functionals defined on partitions of sets of finite perimeter, II: semicontinuity, relaxation and homogenization (1990)

*3 dec 2014:*Characterizations of sets of finite perimeter: old and recent results*13 feb 2013:*Spazi di Sobolev in spazi metrici di misura: risultati recenti e problemi aperti*9 nov 2011:*On weak notions of gradient in metric measure spaces*17 nov 2010:*Alcuni problemi di Teoria Geometrica della Misura in spazi Gaussiani*19 may 2010:*Recenti sviluppi della teoria dei perimetri in spazi Gaussiani*28 jan 2009:*Disuguaglianze isoperimetriche e teoria delle correnti*16 feb 2006:*Equazioni di evoluzione di tipo Hamiltoniano nello spazio delle misure di probabilita'*15 nov 2004:*Evolution problems for polyconvex functionals*15 oct 2003:*Problema di Cauchy per campi a variazione limitata e applicazioni*27 feb 2003:*Recenti sviluppi sulla congettura di De Giorgi per le soluzioni intere di equazioni ellittiche semilineari*1 dec 2000:*Funzione distanza, soluzioni viscose e moto per curvatura media*17 nov 2000:*Funzione distanza, soluzioni viscose e moto per curvatura media