# Regularity in kinetic formulations via averaging lemmas

Pierre-Emmanuel Jabin; Benoît Perthame

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 8, page 761-774
- ISSN: 1292-8119

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topJabin, Pierre-Emmanuel, and Perthame, Benoît. "Regularity in kinetic formulations via averaging lemmas." ESAIM: Control, Optimisation and Calculus of Variations 8 (2010): 761-774. <http://eudml.org/doc/90670>.

@article{Jabin2010,

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.
},

author = {Jabin, Pierre-Emmanuel, Perthame, Benoît},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Regularizing effects; kinetic formulation; averaging lemmas; hyperbolic equations; line-energy
Ginzburg–Landau.; isentropic gas dynamics; transport equation},

language = {eng},

month = {3},

pages = {761-774},

publisher = {EDP Sciences},

title = {Regularity in kinetic formulations via averaging lemmas},

url = {http://eudml.org/doc/90670},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Jabin, Pierre-Emmanuel

AU - Perthame, Benoît

TI - Regularity in kinetic formulations via averaging lemmas

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 8

SP - 761

EP - 774

AB -
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.

LA - eng

KW - Regularizing effects; kinetic formulation; averaging lemmas; hyperbolic equations; line-energy
Ginzburg–Landau.; isentropic gas dynamics; transport equation

UR - http://eudml.org/doc/90670

ER -

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