Green's functions for parabolic systems of second order in time-varying domains

Hongjie Dong, Seick Kim

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We construct Green's functions for divergence form, second order parabolic systems in non-smooth time-varying domains whose boundaries are locally represented as graph of functions that are Lipschitz continuous in the spatial variables and 1/2-Hölder continuous in the time variable, under the assumption that weak solutions of the system satisfy an interior Hölder continuity estimate. We also derive global pointwise estimates for Green's function in such time-varying domains under the assumption that weak solutions of the system vanishing on a portion of the boundary satisfy a certain local boundedness estimate and a local Hölder continuity estimate. In particular, our results apply to complex perturbations of a single real equation.

Original languageEnglish
Pages (from-to)1407-1433
Number of pages27
JournalCommunications on Pure and Applied Analysis
Volume13
Issue number4
DOIs
Publication statusPublished - 2014 Jul

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Green's functions for parabolic systems of second order in time-varying domains'. Together they form a unique fingerprint.

  • Cite this