Full Professor, Departement Mathematik und Informatik, Universität Basel

Email: gianluca.crippa AT unibas.ch

Home-page: https://dmi.unibas.ch/en/persons/gianluca-crippa/

Available papers (51):

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• G. Crippa - G. Stefani (Calc. Var. Partial Differential Equations)
  An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces (2024)
• G. M. Coclite - M. Colombo - G. Crippa - N. De Nitti - A. Keimer - E. Marconi - L. Pflug - L. V. Spinolo (Submitted Paper)
  Oleĭnik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit (2023)
• G. Crippa - M. Inversi - C. Saffirio - G. Stefani (Accepted Paper: Nonlinearity)
  Existence and stability of weak solutions of the Vlasov-Poisson system in localized Yudovich spaces (2023)
• E. Bruè - M. Colombo - G. Crippa - C. De Lellis - M. Sorella (Communications on Pure and Applied Analysis)
  Onsager critical solutions of the forced Navier-Stokes equations (2022)
• M. Colombo - G. Crippa - E. Marconi - L. V. Spinolo (Preprint)
  Nonlocal traffic models with general kernels: singular limit, entropy admissibility, and convergence rate (2022)
• M. Colombo - G. Crippa - E. Marconi - L. V. Spinolo (Accepted Paper: Ann. de l'institute H. Poincaré, Analyse non linéaire)
  Local limit of nonlocal traffic models: convergence results and total variation blow-up (2021)
• 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. 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)
• 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)
• 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 (Journal of Differential Equations)
  Lagrangian solutions to the Vlasov-Poisson system with L^1 density (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)
• 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 - L. Ambrosio - G. Crippa - G. Crippa - A. Figalli - A. Figalli - L. V. Spinolo - L. V. Spinolo (IMA Vol. Math. Appl.)
  Existence and uniqueness results for the continuity equation and applications to the chromatography system (2011)
• L. Ambrosio - L. Ambrosio - G. Crippa - G. Crippa - A. Figalli - A. Figalli - L. V. Spinolo - L. V. Spinolo (IMA Vol. Math. Appl.)
  Existence and uniqueness results for the continuity equation and applications to the chromatography system (2011)
• 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)

Seminars:

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

Speaker:

• 30 jun 2025 - 4 jul 2025: Topics in Geometric Measure Theory
• 28 jun 2023 - 30 jun 2023: Geometrical trends in Applied Analysis

Organizer:

• 21 jul 2025 - 23 jul 2025: CoScaRa Workshop: Deterministic and Stochastic Advection in Fluid Dynamics
• 8 jul 2019 - 10 jul 2019: GMT and PDEs in Basel – A young researchers meeting
• 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