A Weighted Sobolev Space Theory of Parabolic Stochastic PDEs on Non-smooth Domains

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Abstract

In this article, we study parabolic stochastic partial differential equations (see Eq. (1.1)) defined on arbitrary bounded domain O ⊂ ℝd admitting the Hardy inequality (Formula Presented) where ρ (x)= dist(x,∂ O). Existence and uniqueness results are given in weighted Sobolev spaces (Formula Presented) where p ∈ [2,∞), γ ∈ ℝ is the number of derivatives of solutions and θ controls the boundary behavior of solutions (see Definition 2.5). Furthermore, several Hölder estimates of the solutions are also obtained. It is allowed that the coefficients of the equations blow up near the boundary.

Original languageEnglish
Pages (from-to)107-136
Number of pages30
JournalJournal of Theoretical Probability
Volume27
Issue number1
DOIs
Publication statusPublished - 2014 Mar 1

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Keywords

  • Hardy inequality
  • L-theory
  • Non-smooth domain
  • Stochastic partial differential equation
  • Weighted Sobolev space

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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