A Wp n-theory of parabolic equations with unbounded leading coefficients on non-smooth domains

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We study parabolic partial differential equations with unbounded second-, first- and zero-order coefficients on non-smooth domains allowing Hardy inequality. 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 nonnegative real number, in particular, it can be fractional.

Original languageEnglish
Pages (from-to)294-305
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 2009 Feb 1



  • Hardy inequality
  • Non-smooth domains
  • Unbounded leading coefficients
  • Weighted Sobolev spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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