Displaying similar documents to “Regularity in kinetic formulations via averaging lemmas”

Regularity in kinetic formulations via averaging lemmas

Pierre-Emmanuel Jabin, Benoît Perthame (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

New Results in Velocity Averaging

François Golse (2001-2002)

Séminaire Équations aux dérivées partielles

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This paper discusses two new directions in velocity averaging. One is an improvement of the known velocity averaging results for L 1 functions. The other shows how to adapt some of the ideas of velocity averaging to a situation that is essentially a new formulation of the Vlasov-Maxwell system.

Some regularizing methods for transport equations and the regularity of solutions to scalar conservation laws

Pierre-Emmanuel Jabin (2008-2009)

Séminaire Équations aux dérivées partielles

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We study several regularizing methods, stationary phase or averaging lemmas for instance. Depending on the regularity assumptions that are made, we show that they can either be derived one from the other or that they lead to different results. Those are applied to Scalar Conservation Laws to precise and better explain the regularity of their solutions.