Boundary Value Problems for Parabolic Operators in a Time-Varying Domain

Sungwon Cho; Hongjie Dong; Doyoon Kim

doi:10.1080/03605302.2015.1019628

Boundary Value Problems for Parabolic Operators in a Time-Varying Domain

Sungwon Cho, Hongjie Dong, Doyoon Kim

Research output: Contribution to journal › Article

1 Citation (Scopus)

Abstract

We prove the existence of unique solutions to Dirichlet boundary value problems for linear second-order uniformly parabolic operators in either divergence or non-divergence form with boundary blowup low-order coefficients. The domain is possibly time varying, non-smooth, and satisfies an exterior measure condition.

Original language	English
Pages (from-to)	1282-1313
Number of pages	32
Journal	Communications in Partial Differential Equations
Volume	40
Issue number	7
DOIs	https://doi.org/10.1080/03605302.2015.1019628
Publication status	Published - 2015 Jul 3
Externally published	Yes

Keywords

Blowup low-order coefficients
Exterior measure condition
Parabolic Dirichlet boundary value problems
Time-varying domain
Vanishing mean oscillation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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abstract = "We prove the existence of unique solutions to Dirichlet boundary value problems for linear second-order uniformly parabolic operators in either divergence or non-divergence form with boundary blowup low-order coefficients. The domain is possibly time varying, non-smooth, and satisfies an exterior measure condition.",

keywords = "Blowup low-order coefficients, Exterior measure condition, Parabolic Dirichlet boundary value problems, Time-varying domain, Vanishing mean oscillation",

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KW - Time-varying domain

KW - Vanishing mean oscillation

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