Regularity in kinetic formulations via averaging lemmas

Jabin, Pierre-Emmanuel; Perthame, Benoît

doi:10.1051/cocv:2002033

Jabin, Pierre-Emmanuel ; Perthame, Benoît

ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 761-774.

Résumé

We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particular they improve the known regularity for systems like $γ = 3$ in isentropic gas dynamics or in some variational problems arising in thin micromagnetic films. They also allow to obtain directly the best known regularizing effect in multidimensional scalar conservation laws. The new ingredient here is to use velocity regularity for the solution to the transport equation under consideration. The method of proof is based on a decomposition of the density in Fourier space, combined with the $K$ -method of real interpolation.

MR Zbl | 5 citations dans Numdam

DOI : 10.1051/cocv:2002033

Classification : 35L65, 35B30, 35B65, 74G65, 83D30
Mots-clés : regularizing effects, kinetic formulation, averaging lemmas, hyperbolic equations, line-energy Ginzburg-Landau

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     title = {Regularity in kinetic formulations via averaging lemmas},
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     pages = {761--774},
     publisher = {EDP-Sciences},
     volume = {8},
     year = {2002},
     doi = {10.1051/cocv:2002033},
     mrnumber = {1932972},
     zbl = {1065.35185},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/cocv:2002033/}
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Jabin, Pierre-Emmanuel; Perthame, Benoît. Regularity in kinetic formulations via averaging lemmas. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 761-774. doi : 10.1051/cocv:2002033. https://www.numdam.org/articles/10.1051/cocv:2002033/

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