Sobolev estimates for non-uniformly parabolic PDEs

Steve Schochet

doi:10.1007/s42985-022-00149-4

Sobolev estimates for non-uniformly parabolic PDEs

Steve Schochet

School of Mathematical Sciences

Tel Aviv University

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

Abstract

Sobolev energy estimates are proven for solutions of initial-value-problems for non-uniformly parabolic second-order PDEs having symmetric coefficients depending on the independent and dependent variables. Local-in-time existence of solutions to initial-value problems for such systems and convergence results for singular limits involving such systems are consequences of those uniform bounds.

Original language	English
Article number	13
Journal	Partial Differential Equations and Applications
Volume	3
Issue number	1
DOIs	https://doi.org/10.1007/s42985-022-00149-4
State	Published - Feb 2022

Keywords

Non-uniformly parabolic
Sobolev energy estimates
singular limit

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics
Computational Mathematics
Numerical Analysis

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10.1007/s42985-022-00149-4

Cite this

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title = "Sobolev estimates for non-uniformly parabolic PDEs",

abstract = "Sobolev energy estimates are proven for solutions of initial-value-problems for non-uniformly parabolic second-order PDEs having symmetric coefficients depending on the independent and dependent variables. Local-in-time existence of solutions to initial-value problems for such systems and convergence results for singular limits involving such systems are consequences of those uniform bounds.",

keywords = "Non-uniformly parabolic, Sobolev energy estimates, singular limit",

author = "Steve Schochet",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2022",

month = feb,

doi = "10.1007/s42985-022-00149-4",

language = "الإنجليزيّة",

volume = "3",

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N2 - Sobolev energy estimates are proven for solutions of initial-value-problems for non-uniformly parabolic second-order PDEs having symmetric coefficients depending on the independent and dependent variables. Local-in-time existence of solutions to initial-value problems for such systems and convergence results for singular limits involving such systems are consequences of those uniform bounds.

AB - Sobolev energy estimates are proven for solutions of initial-value-problems for non-uniformly parabolic second-order PDEs having symmetric coefficients depending on the independent and dependent variables. Local-in-time existence of solutions to initial-value problems for such systems and convergence results for singular limits involving such systems are consequences of those uniform bounds.

KW - Non-uniformly parabolic

KW - Sobolev energy estimates

KW - singular limit

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U2 - 10.1007/s42985-022-00149-4

DO - 10.1007/s42985-022-00149-4

M3 - مقالة

SN - 2662-2963

VL - 3

JO - Partial Differential Equations and Applications

JF - Partial Differential Equations and Applications

IS - 1

M1 - 13

ER -

Sobolev estimates for non-uniformly parabolic PDEs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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