[crippa]

Associate Professor, Departement Mathematik und Informatik, Universität Basel

**Email:** *gianluca.crippa AT unibas.ch*

**Home-page:** http://www.math.unibas.ch/crippa

- G. Alberti - G. Crippa - A. L. Mazzucato (Submitted Paper)

Loss of regularity for the continuity equation with non-Lipschitz velocity field (2018) - G. Alberti - G. Crippa - A. L. Mazzucato (Accepted Paper:
*Journal of the American Mathematical Society*)

Exponential self-similar mixing by incompressible flows (2018) - S. Bianchini - M. Colombo - G. Crippa - L. V. Spinolo (Submitted Paper)

Optimality of integrability estimates for advection-diffusion equations (2017) - M. Colombo - G. Crippa - L. V. Spinolo (Preprint)

On the singular local limit for conservation laws with nonlocal fluxes (2017) - A. Bohun - F. Bouchut - G. Crippa (
*Nonlinear Analysis: Theory, Methods & Applications*)

Lagrangian solutions to the 2D Euler system with $L^1$ vorticity and infinite energy (2016) - A. P. Choudhury - G. Crippa - L. V. Spinolo (Submitted Paper)

Initial-boundary value problems for nearly incompressible vector ﬁelds, and applications to the Keyﬁtz and Kranzer system (2016) - L. Caravenna - G. Crippa (Accepted Paper:
*C. R. Math. Acad. Sci. Paris*)

Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation (2016) - M. Colombo - G. Crippa - S. Spirito (Accepted Paper:
*Calc. Var. PDE*)

Renormalized solutions to the continuity equation with an integrable damping term (2015) - A. Bohun - F. Bouchut - G. Crippa (
*Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire*)

Lagrangian flows for vector fields with anisotropic regularity (2015) - A. Bohun - F. Bouchut - G. Crippa (
*Journal of Differential Equations*)

Lagrangian solutions to the Vlasov-Poisson system with L^1 density (2015) - G. Alberti - S. Bianchini - G. Crippa (
*Journal of the European Mathematical Society (JEMS)*)

A uniqueness result for the continuity equation in two dimensions (2014) - G. Crippa - C. Donadello - L. V. Spinolo (
*Journal de Mathematiques Pures et Appliquees*)

Initial-boundary value problems for continuity equations with $BV$ coefficients (2014) - G. Crippa - S. Spirito (Submitted Paper)

Renormalized Solutions of the 2D Euler Equations (2014) - G. Crippa - N. Gusev - S. Spirito - E. Wiedemann (Submitted Paper)

Failure of the Chain Rule for the Divergence of Bounded Vector Fields (2014) - G. Crippa - N. Gusev - S. Spirito - E. Wiedemann (Submitted Paper)

Non-uniqueness and prescribed energy for the continuity equation (2014) - L. Ambrosio - G. Crippa (
*Proceedings of the Royal Society of Edinburgh: Section A*)

Continuity equations and ODE flows with non-smooth velocity (2014) - G. Alberti - G. Crippa - A. L. Mazzucato (
*Comptes Rendus Mathématique*)

Exponential self-similar mixing and loss of regularity for continuity equations (2014) - G. Crippa - M. C. Lopes Filho - E. Miot - H. J. Nussenzveig Lopes (Submitted Paper)

Flows of vector fields with point singularities and the vortex-wave system (2013) - G. Crippa - C. Donadello - L. V. Spinolo (Proceedings)

A note on the initial-boundary value problem for continuity equations with rough coefficients (2013) - G. Crippa (Proceedings)

Ordinary Differential Equations and Singular Integrals (2013) - G. Alberti - S. Bianchini - G. Crippa (
*Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5)*)

Structure of level sets and Sard-type properties of Lipschitz maps (2013) - F. Bouchut - G. Crippa (
*J. Hyper. Differential Equations*)

Lagrangian flows for vector fields with gradient given by a singular integral (2013) - E. Acerbi - G. Crippa - D. Mucci (
*ESAIM: Control, Optimisation and Calculus of Variations*)

A variational problem for couples of functions and multifunctions with interaction between leaves (2012) - G. Alberti - S. Bianchini - G. Crippa (Accepted Paper:
*Revista Matemática Iberoamericana*)

On the L^p differentiability of certain classes of functions (2012) - G. Crippa (
*Journal of Differential Equations*)

Lagrangian flows and the one dimensional Peano phenomenon for ODEs (2011) - G. Crippa - M. Lecureux-Mercier (Accepted Paper:
*Nonlinear Differential Equations and Applications NoDEA*)

Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow (2011) - 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) - G. Crippa - L. V. Spinolo (
*Communications on Pure and Applied Analysis*)

An overview on some results concerning the transport equation and its applications to conservation laws (2010) - 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) - G. Crippa - C. Jimenez - A. Pratelli (
*Advances in Calculus of Variations*)

Optimum and equilibrium in a transport problem with queue penalization effect (2009) - F. Bouchut - G. Crippa (
*Séminaire Équations aux dérivées partielles (Polytechnique)*)

Equations de transport à coefficient dont le gradient est donné par une intégrale singulière (2009) - G. Crippa - C. Jimenez - A. Pratelli (
*Singularities in nonlinear evolution phenomena and applications - proceedings*)

A transport problem with queue penalization effect (2009) - L. Ambrosio - G. Crippa - P. G. LeFloch (
*Netw. Heterog. Media*)

Leaf superposition property for integer rectifiable currents (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) - G. Crippa - C. De Lellis (
*J. Reine Angew. Math.*)

Estimates and regularity results for the DiPerna--Lions flow (2008) - G. Crippa - F. Otto - M. Westdickenberg (
*In: Transport Equations and Multi-D Hyperbolic Conservation Laws, Lecture Notes of the Unione Matematica Italiana*)

Regularizing effect of nonlinearity in multidimensional scalar conservation laws (2008) - G. Crippa - C. De Lellis (
*Hyperbolic Problems: Theory, Numerics, Applications*)

Regularity and compactness for the DiPerna--Lions flow (2008) - G. Crippa (
*Boll. Unione Mat. Ital. (9)*)

The ordinary differential equation with non-Lipschitz vector fields (2008) - G. Crippa (Ph.D. Thesis)

The flow associated to weakly differentiable vector fields (2007) - F. Colombini - G. Crippa - J. Rauch (
*Comm. Partial Differential Equations*)

A note on two dimensional transport with bounded divergence (2006) - F. Bouchut - G. Crippa (
*SIAM J. Math. Anal.*)

Uniqueness, renormalization and smooth approximations for linear transport equations (2006) - G. Crippa - C. De Lellis (
*Indiana Univ. Math. J.*)

Oscillatory solutions to transport equations (2006) - 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) - G. Crippa (Degree Thesis)

Equazione del trasporto e problema di Cauchy per campi vettoriali debolmente differenziabili (2004)

*6 apr 2006:*Regularity and compactness for the flow associated to weakly differentiable vector fields*4 may 2005:*Soluzioni oscillanti di equazioni di trasporto

*26 jun 2017 - 30 jun 2017:*Irregular Transport: Analysis and Applications*1 nov 2016 - 4 nov 2016:*Transport phenomena in collective dynamics: from micro to social hydrodynamics: A joint FIM-KiNet conference*19 oct 2016 - 21 oct 2016:*Workshop on Recent Trends in the Analysis of PDEs*18 jul 2016 - 22 jul 2016:*GSSI Summer School on Fluid Dynamics and Related Topics*20 jul 2015 - 24 jul 2015:*SUMMER SCHOOL ON TRANSPORT, FLUIDS AND MIXING*23 jun 2014 - 18 jul 2014:*Summer School on Geometric Measure Theory and Geometric Analysis*12 feb 2013 - 14 feb 2013:*Basel Junior Symposium in Analysis