An L p -theory of SPDEs on Lipschitz domains

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Abstract

Stochastic partial differential equations are considered on Lipschitz domains. Existence and uniqueness results are given in weighted Sobolev spaces, and Hölder estimates of the solutions are also obtained. The number of derivatives of the solutions can be any real number, in particular, it can be negative and fractional. It is allowed that the coefficients of the equations blow up near the boundary.

Original languageEnglish
Pages (from-to)303-326
Number of pages24
JournalPotential Analysis
Volume29
Issue number3
DOIs
Publication statusPublished - 2008 Nov 1

Keywords

  • Lipschitz domains
  • Stochastic partial differential equations
  • Weighted Sobolev spaces

ASJC Scopus subject areas

  • Analysis

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