COMMUTATOR METHOD FOR AVERAGING LEMMAS

Pierre Emmanuel Jabin; Hsin Yi Lin; Eitan Tadmor

doi:10.2140/apde.2022.15.1561

COMMUTATOR METHOD FOR AVERAGING LEMMAS

Pierre Emmanuel Jabin, Hsin Yi Lin, Eitan Tadmor

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We introduce a commutator method with multiplier to prove averaging lemmas, the regularizing effect for the velocity average of solutions for kinetic equations. Our method requires only elementary techniques in Fourier analysis and highlights a new range of assumptions that are sufficient for the velocity average to be in (Formula Presented). Our result provides a direct proof (without interpolation) and improves the regularizing result for the measure-valued solutions to scalar conservation laws in space dimension 1.

Original language	English (US)
Pages (from-to)	1561-1584
Number of pages	24
Journal	Analysis and PDE
Volume	15
Issue number	6
DOIs	https://doi.org/10.2140/apde.2022.15.1561
State	Published - 2022

All Science Journal Classification (ASJC) codes

Analysis
Numerical Analysis
Applied Mathematics

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10.2140/apde.2022.15.1561

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abstract = "We introduce a commutator method with multiplier to prove averaging lemmas, the regularizing effect for the velocity average of solutions for kinetic equations. Our method requires only elementary techniques in Fourier analysis and highlights a new range of assumptions that are sufficient for the velocity average to be in (Formula Presented). Our result provides a direct proof (without interpolation) and improves the regularizing result for the measure-valued solutions to scalar conservation laws in space dimension 1.",

author = "Jabin, {Pierre Emmanuel} and Lin, {Hsin Yi} and Eitan Tadmor",

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AB - We introduce a commutator method with multiplier to prove averaging lemmas, the regularizing effect for the velocity average of solutions for kinetic equations. Our method requires only elementary techniques in Fourier analysis and highlights a new range of assumptions that are sufficient for the velocity average to be in (Formula Presented). Our result provides a direct proof (without interpolation) and improves the regularizing result for the measure-valued solutions to scalar conservation laws in space dimension 1.

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COMMUTATOR METHOD FOR AVERAGING LEMMAS

Abstract

All Science Journal Classification (ASJC) codes

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