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

Sungwon Cho, Hongjie Dong, Doyoon Kim

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)1282-1313
Number of pages32
JournalCommunications in Partial Differential Equations
Volume40
Issue number7
DOIs
Publication statusPublished - 2015 Jul 3
Externally publishedYes

Bibliographical note

Funding Information:
S. Cho was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2012-0003253). H. Dong was partially supported by the NSF under agreement DMS-1056737. D. Kim was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2054865).

Publisher Copyright:
© 2015, Taylor & Francis Group, LLC.

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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