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PDE, 29 , — Ambrosio, G.


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Maniglia: Traces and fine properties of a BD class of vector fields and applications. Toulouse, XIV 4 , — MathSciNet Google Scholar. De Lellis: Existence of solutions for a class of hyperbolic systems of conservation laws in several space dimensions. International Mathematical Research Notices, 41 , — Ambrosio, C. Ambrosio, N. Pallara: Functions of bounded variation and free discontinuity problems.

Oxford Mathematical Monographs, Ambrosio, M. Maniglia: Lipschitz regularity and approximate differentiability of the DiPerna—Lions flow. Rendiconti del Seminario Fisico Matematico di Padova, , 29— Ambrosio, S.

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Manuscripta Math. Proceedings of the Royal Society of Edinburgh, A , — Balder: New fundamentals of Young measure convergence. CRC Res. Notes in Math.

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James: Fine phase mixtures as minimizers of energy. Bangert: Minimal measures and minimizing closed normal one-currents. Brenier: Weak solutions for the semigeostrophic equation formulated as a couples Monge-Ampere transport problem. SIAM J. Buffoni: Optimal mass transportation and Mather theory.

JEMS , 9 , 85— Bernot, V. Morel: Traffic plans. Wolf: Absolutely continuous flows generated by Sobolev class vector fields in finite and infinite dimensions. Bouchut: Renormalized solutions to the Vlasov equation with coefficients of bounded variation. Rational Mech. Bouchut, F. Pulvirenti: Kinetic equations and asymptotic theory. Series in Appl. James: One dimensional transport equation with discontinuous coefficients.

Nonlinear Analysis, 32 , — Mancini: Uniqueness and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficients. Annali Scuola Normale Superiore, Ser.


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Brenier: The least action principle and the related concept of generalized flows for incompressible perfect fluids. Brenier: The dual least action problem for an ideal, incompressible fluid. Brenier: A homogenized model for vortex sheets. Brenier: Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations.

Bressan: An ill posed Cauchy problem for a hyperbolic system in two space dimensions. Padova, , — Brezis: Analyse fonctionnelle. Masson, Paris, Caffarelli: Boundary regularity of maps with convex potentials , Comm. Caffarelli: The regularity of mappings with a convex potential.

The Flow Associated to Weakly Differentiable Vector Fields | Gianluca Crippa | Springer

Caffarelli: Boundary regularity of maps with convex potentials. Sci Appl. Cellina: On uniqueness almost everywhere for monotonic differential inclusions. Nonlinear Analysis, TMA, 25 , — Vornicescu: On gradient flows. Journal of Differential Equations, , — Colombini, G. Rauch: A note on two dimensional transport with bounded divergence. Partial Differential Equations, 31 , — Lerner: Uniqueness of continuous solutions for BV vector fields.

Duke Math. Colombini, T. Rauch: Nearly Lipschitzean diverge free transport propagates neither continuity nor BV regularity. De Lellis: Oscillatory solutions to transport equations. Indiana Univ. Accepted by J.

About this book

Reine Angew. Cullen: On the accuracy of the semi-geostrophic approximation. CrossRef Google Scholar. Feldman: Lagrangian solutions of semigeostrophic equations in physical space. Gangbo: A variational approach for the 2-dimensional semi-geostrophic shallow water equations.

Dafermos: Hyperbolic conservation laws in continuum physics. Springer Verlag, De Pascale, M. E-mail address: thierry. Use the link below to share a full-text version of this article with your friends and colleagues. Learn more. In this paper we study the semiclassical limit of the Schrodinger equation. In order to achieve this goal we prove existence, uniqueness, and stability results for the flow in the space of measures induced by the continuity equation.

Volume 64 , Issue 9. The full text of this article hosted at iucr. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account. If the address matches an existing account you will receive an email with instructions to retrieve your username. Luigi Ambrosio E-mail address: l. Alessio Figalli E-mail address: figalli math.

The flow associated to weakly differentiable vector fields

Gero Friesecke E-mail address: gf ma. Johannes Giannoulis E-mail address: giannoul ma. Thierry Paul E-mail address: thierry.

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