Regularity in kinetic formulations Via averaging lemmas

Pierre Emmanuel Jabin, Benoît Perthame

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)761-774
Number of pages14
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume8
DOIs
StatePublished - Jun 2002

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics

Fingerprint Dive into the research topics of 'Regularity in kinetic formulations Via averaging lemmas'. Together they form a unique fingerprint.

Cite this