L. Ambrosio, A. Braides:
Functionals defined on partitions of sets of finite perimeter, I: integral representation and $\Gamma$-convergence
J. Math. Pures. Appl. Vol. 69, p. 285-305, 1990
L. Ambrosio, A. Braides:
Functionals defined on partitions of sets of finite perimeter, II: semicontinuity, relaxation and homogenization
J. Math. Pures. Appl. Vol. 69, p. 307-333, 1990
L. Ambrosio, A. Braides, A. Garroni:
Special functions with bounded variation and with weakly differentiable traces on the jump set
(partially unpublished manuscript) 1995
G. Alberti, L. Ambrosio:
A Geometrical Approach to Monotone Functions in ${\mathbb R}^n$
Math. Zeit. Vol. 230 (1999), p. 259-316, 1996
L. Ambrosio, A. Coscia, G. Dal Maso:
Fine Properties of Functions with Bounded Deformation
Arch. Rational Mech. Anal. Vol. 139, p. 201-238, 1997
L. Ambrosio, D. Pallara:
Partial Regularity of Free Discontinuity Sets I
Annali della Scuola Normale Superiore di Pisa 1997
L. Ambrosio, N. Fusco, D. Pallara:
Partial Regularity of Free Discontinuity Sets II
Annali della Scuola Normale Superiore di Pisa 1997
L. Ambrosio, A. Braides:
Energies in SBV and variational models in fracture mechanics.
Homogenization and Applications to Material Sciences, (D. Cioranescu, A. Damlamian, P. Donato eds.) GAKUTO, Gakkotosho, Tokio, Japan (Paper in Volume) p. 1-22, 1997
L. Ambrosio, I. Fonseca, P. Marcellini, L. Tartar:
On a Volume Constrained Variational Problem
To appear on Arch. Rat. Mech. Anal. () 1998
L. Ambrosio, C. Mantegazza:
Curvature and Distance Function from a Manifold
J. Geom. Anal. Vol. 8, p. 723-748, 1998
L. Ambrosio, M. Gobbino, D. Pallara:
Approximation problems for curvature varifolds
J. Geom. Anal. Vol. 8, p. 1-19, 1998
L. Ambrosio, N. Fusco, D. Pallara:
Higher Regularity of Solutions of Free Discontinuity Problems
Diff. Int. Eqs. 1999
L. Ambrosio, E. Paolini:
Partial regularity for quasi minimizers of perimeter
Ricerche di Matematica Vol. 48, N. supplemento, p. 167-186, 1999
L. Ambrosio, B. Kirchheim:
Rectifiable Sets in Metric and Banach Spaces
Submitted to Math. Annalen. () 1999
L. Ambrosio, C. De Lellis, C. Mantegazza:
Line Energies for Gradient Vector Fields in the Plane
Calc. Var. Vol. 9, p. 327-355, 1999
L. Ambrosio, P. Colli Franzone, G. Savaré:
Gamma-Convergence of a Family of Anisotropic Functionals with Lack of Coercivity
Interfaces and Free Boundaries N. 2, p. 213-266, 2000
L. Ambrosio:
Lecture Notes on Optimal Transport Problems
(Lecture Notes) 2000
G. Alberti, L. Ambrosio, X. Cabrè:
On a long standing conjecture of E. De Giorgi: old and recent results
Acta Appl. Math. Vol. 65 (2001), N. 1, p. 9-33, 2000
L. Ambrosio, X. Cabrè:
Entire Solutions of a Semilinear Elliptic Equation in ${\mathcal R}^3$ and a Conjecture of De Giorgi
Journal of the AMS N. 13, p. 725-739, 2000
L. Ambrosio, B. Kirchheim:
Currents in Metric Spaces
Acta Mathematica N. 185, p. 1-80, 2000
L. Ambrosio:
Some Fine Properties of Sets of Finite Perimeter in Ahlfors Regular Metric Measure Spaces
Advances in Mathematics N. 159, p. 51-67, 2001
L. Ambrosio, V. Caselles, S. Masnou, J. M. Morel:
Connected Components of Sets of Finite Perimeter and Applications to Image Processing
Journal of EMS. N. 3, p. 213-266, 2001
L. Ambrosio, L. Faina, R. March:
Variational Approximation of a Second Order Free Discontinuity Problem in Computer Vision
SIAM J. Math. Anal. N. 32, p. 1171-1197, 2001
L. Ambrosio, M. Lecumberry, T. Riviere:
A viscosity property of minimizing micromagnetic configurations
Communications on Pure and Applied Mathematics (Accepted Paper) 2002
L. Ambrosio, B. Kirchheim, M. Lecumberry, T. Riviere:
On the rectifiability of defect measures arising in a micromagnetics model
p. 29-60, 2002
L. Ambrosio, S. Masnou:
A direct variational approach to a problem arising in image reconstruction
Interfaces and Free Boundaries (Accepted Paper) 2002
L. Ambrosio:
Fine properties of sets of finite perimeter in doubling metric measure spaces
Set Valued Analysis Vol. 10, p. 111-128, 2002
L. Ambrosio, M. Novaga, E. Paolini:
Some Regularity Results for Minimal Crystals
ESAIM: COCV volume dedicated to J. L. Lions Vol. 8, N. 69--103, 2002
L. Ambrosio, S. Rigot:
Optimal Mass Transportation in the Heisenberg Group
Journal of Functional Analysis (Accepted Paper) 2002
L. Ambrosio, A. Pratelli:
Existence and stability results in the $L^1$ theory of optimal transportation
2002
L. Ambrosio:
Transport equation and Cauchy problem for BV vector fields
Inventiones Mathematicae (Accepted Paper) 2003
L. Ambrosio, C. De Lellis:
Existence of solutions for a class of hyperbolic systems of conservation laws in several space dimensions
International Mathematics Research Notices N. 41, p. 2205-2220, 2003
L. Ambrosio, N. Gigli, G. Savaré:
Gradient flows with metric and differentiable structures, and applications to the Wasserstein space
(Accepted Paper) 2003
L. Ambrosio, V. Magnani:
Weak differentiability of BV functions on stratified groups
Math. Z. Vol. 245, p. 123-153, 2003
L. Ambrosio, F. Bouchut, C. De Lellis:
Well--posedness for a class of hyperbolic systems of conservation laws in several space dimensions
Comm. Partial Differential Equations Vol. 29, N. 9--10, p. 1635-1671, 2004
L. Ambrosio, B. Kirchheim, A. Pratelli:
Existence of optimal transport maps for crystalline norms
Duke Math. J. Vol. 125, N. 2, p. 207-241, 2004
L. Ambrosio, M. Miranda Jr, D. Pallara:
Special Functions of Bounded Variation in Doubling Metric Measure Spaces
Quad. Mat. Vol. 14, p. 1-45, 2004
L. Ambrosio, C. De Lellis:
A note on admissible solutions of 1d scalar conservation laws and 2d Hamilton-Jacobi equations
J. Hyperbolic Diff. Equ. Vol. 1, N. 4, p. 813-826, 2004
L. Ambrosio:
Lecture notes on transport equation and Cauchy problem for $BV$ vector fields and applications
(Lecture Notes) 2004
L. Ambrosio, J. Malý:
Very weak notions of differentiability
(Submitted Paper) 2005
L. Ambrosio, G. Crippa, S. Maniglia:
Traces and fine properties of a $BD$ class of vector fields and applications
Ann. Fac. Sci. Toulouse Math. (6) Vol. 14, N. 4, p. 527-561, 2005
L. Ambrosio:
Steepest descent flows and applications to spaces of probability measures
(Accepted Paper) 2005
L. Ambrosio, H. Frid:
Multiscale Young measures in almost periodic homogenization and applications
(Submitted Paper) 2005
L. Ambrosio, M. Lecumberry, S. Maniglia:
Lipschitz regularity and approximate differentiability of the DiPerna-Lions flow
(Submitted Paper) 2005
L. Ambrosio:
Transport equation and Cauchy problem for non-smooth vector fields
(Preprint) 2005
L. Ambrosio, W. Gangbo:
Hamiltonian ODE's in the Wasserstein space of probability measures
(Submitted Paper) 2005
L. Ambrosio, V. Capasso, E. Villa:
On the approximation of geometric densities of random closed sets
(Submitted Paper) 2006
L. Ambrosio, S. Lisini, G. Savaré:
Stability of flows associated to gradient vector fields and convergence of iterated transport maps
manuscripta math. Vol. 121, p. 1-50, 2006
L. Ambrosio, F. Serra Cassano, D. Vittone:
Intrinsic regular hypersurfaces in Heisenberg groups
J. Geom. Anal. Vol. 16, N. 2, p. 187-232, 2006
L. Ambrosio, F. Santambrogio:
Necessary optimality conditions for geodesics in weighted Wasserstein spaces
Rend. Lincei - Mat. e Appl. Vol. 18, N. 1, p. 23 - 37, 2007
L. Ambrosio, G. Savaré, L. Zambotti:
Existence and Stability for Fokker-Planck equations with log-concave reference measures
Probability Theory and Related Fields (Accepted Paper) 2007
L. Ambrosio, A. Figalli:
On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations
Calc. Var. Partial Differential Equations (Accepted Paper) 2007
L. Ambrosio, A. Colesanti, E. Villa:
One-sided Minkowski content for some classes of closed sets and applications to stochastic geometry
(Submitted Paper) 2007
L. Ambrosio, S. Serfaty:
A gradient flow approach to an evolution problem arising in superconductivity
(Submitted Paper) 2007
L. Ambrosio, A. Figalli:
Geodesics in the space of measure-preserving maps and plans
Arch. Rat. Mech. Anal. (Accepted Paper) 2007
L. Ambrosio, C. De Lellis, J. Malý:
On the chain rule for the divergence of BV like vector fields: applications, partial results, open problems
Perspective in nonlinear partial differential equations p. 31-67, 2007
L. Ambrosio, B. Kleiner, E. Le Donne:
Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane
(Preprint) 2008
L. Ambrosio, G. Crippa, P. G. LeFloch:
Leaf superposition property for integer rectifiable currents
Netw. Heterog. Media Vol. 3, N. 1, p. 85-95, 2008
L. Ambrosio, H. Frid, J. Silva:
Multiscale Young Measures in Homogenization of Continuous Stationary Processes in Compact Spaces and Applications
Journal of Functional Analysis (Accepted Paper) 2008
L. Ambrosio, G. Crippa:
Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields
In: Transport Equations and Multi-D Hyperbolic Conservation Laws, Lecture Notes of the Unione Matematica Italiana Vol. 5, 2008
L. Ambrosio, N. Gigli:
Construction of the parallel transport in the Wasserstein space
Methods and Applications of Analysis (Accepted Paper) 2008
L. Ambrosio, P. Bernard:
Uniqueness of signed measures solving the continuity equation for Osgood vector fields
(Submitted Paper) 2008
L. Ambrosio, A. Figalli:
On flows associated to Sobolev vector fields in Wiener spaces: an approach a' la DiPerna-Lions
J. Funct. Anal. (Accepted Paper) 2008
L. Ambrosio, E. Durand-Cartagena:
Metric differentiability of Lipschitz maps defined on Wiener spaces
Rend. Circ. Mat. Palermo Vol. 2, N. 58, p. 1-10, 2009
L. Ambrosio, G. Crippa, A. Figalli, L. V. Spinolo:
Some new well-posedness results for continuity and transport equations, and applications to the chromatography system
SIAM J. Math. Anal. Vol. 41, N. 5, p. 1890-1920, 2009
L. Ambrosio, M. Scienza:
Locality of the perimeter in Carnot groups and chain rule
(Submitted Paper) 2009
L. Ambrosio, A. Figalli:
Lecture notes on variational models for incompressible Euler equations
(Lecture notes) 2009
L. Ambrosio, M. Katz:
Flat currents modulo $p$ in metric spaces and filling radius inequalities
(Submitted Paper) 2009
L. Ambrosio:
The flow associated to weakly differentiable vector fields: recent results and open problems
(Submitted Paper) 2009
L. Ambrosio, G. Friesecke, J. Giannoulis:
Passage from quantum to classical molecular dynamics in the presence of Coulomb interactions
(Submitted Paper) 2009
L. Ambrosio, S. Wenger:
Rectifiability of flat chains in Banach spaces with coefficients in $*Z*_p$
(Submitted Paper) 2009
L. Ambrosio, S. Maniglia, M. Miranda Jr, D. Pallara:
BV functions in abstract Wiener spaces
J. Funct. Anal. Vol. 258, N. 3, p. 785-813, 2010
L. Ambrosio, S. Maniglia, M. Miranda Jr, D. Pallara:
Towards a theory of BV functions in abstract Wiener spaces
Physica D Vol. 239, N. 15, p. 1458--1429, 2010
L. Ambrosio, G. Crippa, A. Figalli, L. V. Spinolo:
Existence and uniqueness results for the continuity equation and applications to the chromatography system
IMA Vol. Math. Appl., Springer (Proceedings) 2010
L. Ambrosio, A. Figalli:
Surface measures and convergence of the Ornstein-Uhlenbeck semigroup in Wiener spaces
Ann. Fac. Sci. Toulouse Math. (Accepted Paper) 2010
L. Ambrosio, G. Da Prato, D. Pallara:
BV functions in a Hilbert space with respect to a Gaussian measure
Rend. Acc. Lincei 2010
L. Ambrosio, E. Durand-Cartagena:
Stepanov's Theorem in Wiener spaces
(Preprint) 2010
L. Ambrosio, A. Figalli:
Almost everywhere well-posedness of continuity equations with measure initial data
C. R. Math. Acad. Sci. Paris (Accepted Paper) 2010
L. Ambrosio, A. Carlotto, A. Massaccesi:
Lecture Notes on Partial Differential Equations
() 2010
L. Ambrosio, E. Mainini:
Infinite-dimensional porous media equations and optimal transportation
J. Evol. Equ. Vol. 10, p. 217-246, 2010
L. Ambrosio, M. Miranda Jr, D. Pallara:
Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability
Discrete Contin. Dyn. Sys. 2010
L. Ambrosio, A. Lemenant, G. Royer Carfagni:
A variational model for plastic slip and its regularization via Gamma-convergence.
Journal of Elasticity 2010
L. Ambrosio, N. Gigli:
A user's guide to optimal transport
() 2011
L. Ambrosio, A. Figalli, G. Friesecke, J. Giannoulis, T. Paul:
Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data
Comm. Pure Appl. Math. (Accepted Paper) 2011
L. Ambrosio, G. De Philippis, L. Martinazzi:
Gamma-convergence of nonlocal perimeter functionals
Manuscripta Math. Vol. 134, p. 377-403, 2011
L. Ambrosio, G. De Philippis, B. Kirchheim:
Regularity of optimal transport maps and partial differential inclusions
Rend. Lincei - Mat. e Appl. () 2011
L. Ambrosio:
An overview on calculus and heat flow in metric measure spaces and spaces with Riemannian curvature bounded from below
(Proceedings) 2011
L. Ambrosio, E. Mainini, S. Serfaty:
Gradient flow of the Chapman-Rubinstein-Schatzman model for signed vortices
Ann. Inst. H. Poincaré Anal. Non Linéaire Vol. 28, N. 2, p. 217-246, 2011
L. Ambrosio, N. Gigli, G. Savaré:
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
(Submitted Paper) 2011
L. Ambrosio, N. Gigli, G. Savaré:
Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
(Submitted Paper) 2011
L. Ambrosio, N. Gigli, G. Savaré:
Metric measure spaces with Riemannian Ricci curvature bounded from below
(Submitted Paper) 2011
L. Ambrosio, T. Rajala:
Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces
Ann. Mat. Pura Appl. (Accepted Paper) 2012
L. Ambrosio, M. Colombo, G. De Philippis, A. Figalli:
Existence of Eulerian solutions to the semigeostrophic equations in physical space: the 2-dimensional periodic case
Comm. Partial Differential Equations (Accepted Paper) 2012
L. Ambrosio, N. Gigli, G. Savaré:
Heat flow and calculus on metric measure spaces with Ricci curvature bounded below - the compact case
(Preprint) 2012
L. Ambrosio, G. Crasta, V. De Cicco, G. De Philippis:
A nonautonomous chain rule in $W^{1,1}$ and in $BV$
Manuscripta Math. (Accepted Paper) 2012
L. Ambrosio, F. Ghiraldin:
Flat chains with finite size in metric spaces
Ann. Inst. H. Poincaré Anal. Non Linéaire 2012
L. Ambrosio, F. Ghiraldin:
Compactness of special functions of bounded higher variation
Analysis and Geometry in Metric Spaces Vol. 1, p. 130, 2012
L. Ambrosio, M. Colombo, G. De Philippis, A. Figalli:
A global existence result for the semigeostrophic equations in three dimensional convex domains
Discrete Contin. Dyn. Syst. (Accepted Paper) 2012
L. Ambrosio, A. Figalli, E. Runa:
On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces
Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. (Accepted Paper) 2012
L. Ambrosio, N. Gigli, A. Mondino, T. Rajala:
Riemannian Ricci curvature lower bounds in metric measure spaces with $\sigma$-finite measure
Transactions of the AMS (Accepted Paper) 2012
L. Ambrosio, N. Gigli, G. Savaré:
Bakry-Emery curvature-dimension condition and Riemannian Ricci curvature bounds
(Submitted Paper) 2012
L. Ambrosio, G. Da Prato, B. Goldys, D. Pallara:
Bounded variation with respect to a log-concave measure
Comm. P. D. E. Vol. 37, p. 2272-2290, 2012
L. Ambrosio, M. Colombo, S. Di Marino:
Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope
Advanced Studies in Pure Mathematics: "Variational methods for evolving objects" (Accepted Paper) Vol. 67, p. 1-58, 2012
L. Ambrosio, T. Schmidt:
Compactness results for normal currents and the Plateau problem in dual Banach spaces
Proc. Lond. Math. Soc. (3) Vol. 106, N. 5, p. 1121-1142, 2013
L. Ambrosio, J. Feng:
On a class of first order Hamilton-Jacobi equations in metric spaces
(Submitted Paper) 2013
L. Ambrosio, S. Di Marino, G. Savaré:
On the duality between $p$-modulus and probability measures
(Submitted Paper) 2013
L. Ambrosio, S. Di Marino:
Equivalent definitions of $BV$ space and of total variation on metric measure spaces
J. Funct. Anal. Vol. 266, N. 7, p. 4150-4188, 2014
L. Ambrosio, A. Mondino, G. Savaré:
On the Bakry-Èmery condition, the gradient estimates and the Local-to-Global property of $RCD^*(K,N)$ metric measure spaces
Journal of Geometric Analysis (Accepted Paper) 2014
L. Ambrosio, G. Crippa:
Continuity equations and ODE flows with non-smooth velocity
Proceedings of the Royal Society of Edinburgh: Section A Vol. 144, N. 6, p. 1191-1244, 2014
L. Ambrosio, A. Pinamonti, G. Speight:
Tensorization of Cheeger energies, the space $H^{1,1}$ and the area formula for graphs
Advances in Mathematics Vol. 281, N. 1145-1177, 2014
L. Ambrosio, D. Trevisan:
Well posedness of Lagrangian flows and continuity equations in metric
measure spaces
Analysis and PDE Vol. 7, N. 5, p. 1179-1234, 2014
L. Ambrosio:
Regularity theory for mass-minimizing currents (after Almgren-De Lellis-Spadaro)
(Submitted Paper) 2015
L. Ambrosio, J. Bourgain, H. Brezis, A. Figalli:
$BMO$-type norms related to the perimeter of sets
Comm. Pure Appl. Math. (Accepted Paper) 2015
L. Ambrosio, J. Bertrand:
DC Calculus
(Submitted Paper) 2015
L. Ambrosio, C. De Lellis, T. Schmidt:
Partial regularity for mass-minimizing currents in Hilbert spaces
J. Reine Angew. Math. 2015
L. Ambrosio, M. Colombo, A. Figalli:
Existence and uniqueness of maximal regular flows for non-smooth vector fields
Arch. Ration. Mech. Anal. (Accepted Paper) 2015
L. Ambrosio, M. Erbar, G. Savaré:
Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces
(Submitted Paper) 2015
L. Ambrosio, M. Miranda Jr, D. Pallara:
Some fine properties of $BV$ functions on Wiener spaces
Anal. Geom. Metr. Spaces (Accepted Paper) 2015
L. Ambrosio, R. Ghezzi:
Sobolev and Bounded Variation Functions on Metric Measure Spaces
(Submitted Paper) 2015
L. Ambrosio, R. Ghezzi, V. Magnani:
BV functions and sets of finite perimeters in sub-Riemannian manifolds
Ann. Inst. H. Poincaré Anal. Non Linéaire Vol. 32, N. 3, p. 489517, 2015
L. Ambrosio, A. Mondino, G. Savaré:
Nonlinear diffusion equations and curvature conditions in metric measure spaces
Memoirs Amer. Math. Soc. (Accepted Paper) 2015
L. Ambrosio, A. Pinamonti, G. Speight:
Weighted Sobolev Spaces on Metric Measure Spaces
J. Reine Angew. Math. (Accepted paper) 2015
L. Ambrosio, D. Trevisan:
Lecture notes on the DiPerna-Lions theory in abstract measure spaces
(Preprint) 2015
L. Ambrosio, S. Honda:
New stability results for sequences of metric measure spaces with uniform Ricci bounds from below
(Submitted Paper) 2016
L. Ambrosio, D. Puglisi:
Linear extension operators between spaces of Lipschitz maps and Optimal Transport}
(Submitted Paper) 2016
L. Ambrosio, A. Mondino:
Gaussian-type Isoperimetric Inequalities in $RCD(K,\infty)$ probability spaces for positive $K$
Rend. Lincei Mat. Appl. Vol. 27, p. 497514, 2016
L. Ambrosio, G. E. Comi:
Anisotropic surface measures as limits of volume fractions
(Submitted Paper) 2016
L. Ambrosio, S. Di Marino, N. Gigli:
Perimeter as relaxed Minkowski content in metric measure spaces
Nonlinear Analysis: Theory, Methods & Applications (Submitted Paper) Vol. 153, p. 78-88, 2016
L. Ambrosio, F. Stra, D. Trevisan:
A PDE approach to a 2-dimensional matching problem
(Preprint) 2016
L. Ambrosio, F. Stra, D. Trevisan:
Weak and strong convergence of derivations and stability of flows with
respect to MGH convergence
(Submitted Paper) 2016
L. Ambrosio, S. Honda, D. Tewodrose:
Short-time behavior of the heat kernel and Weyl's law on $RCD^*(K,N)$ spaces
(Submitted Paper) 2017
L. Ambrosio, S. Honda:
Local spectral convergence in $RCD^*(K,N)$ spaces
(Submitted Paper) 2017
L. Ambrosio:
Well posedness of ODE's and continuity equations with nonsmooth vector fields, and applications
(Submitted Paper) 2017
L. Ambrosio, M. Colombo, A. Figalli:
On the Lagrangian structure of transport equations: the Vlasov-Poisson system
Duke Math. J. (Accepted Paper) 2017
L. Ambrosio, S. Honda, J. Portegies:
Continuity of nonlinear eigenvalues in $CD(K,\infty)$ spaces with respect to measured Gromov-Hausdorff convergence
(Submitted Paper) 2017