Parabolic equations in simple convex polytopes with time irregular coefficients

Hongjie Dong, Doyoon Kim

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We prove the Wp 1,2-estimate and solvability for the Dirichlet problem of second-order parabolic equations in simple convex polytopes with time irregular coefficients, when p ∈ (1, 2]. We also consider the corresponding Neumann problem in a half space when p ∈ [2, ∞). Similar results are obtained for equations in a half space with coefficients which are measurable in a tangential direction and have small mean oscillations in the other directions. Equations with discontinuous coefficients in nonsmooth domains emerge from problems in mechanics, engineering, and biology, to name a few fields.

Original languageEnglish
Pages (from-to)1789-1819
Number of pages31
JournalSIAM Journal on Mathematical Analysis
Volume46
Issue number3
DOIs
Publication statusPublished - 2014 Jan 1
Externally publishedYes

Fingerprint

Convex Polytopes
Half-space
Parabolic Equation
Irregular
Mechanics
Nonsmooth Domains
Discontinuous Coefficients
Neumann Problem
Coefficient
Second Order Equations
Dirichlet Problem
Biology
Solvability
Oscillation
Engineering
Estimate

Keywords

  • Boundary value problems
  • Measurable coefficients
  • Second-order parabolic equations
  • Simple convex polytopes

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

Parabolic equations in simple convex polytopes with time irregular coefficients. / Dong, Hongjie; Kim, Doyoon.

In: SIAM Journal on Mathematical Analysis, Vol. 46, No. 3, 01.01.2014, p. 1789-1819.

Research output: Contribution to journalArticle

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