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

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2 Citations (Scopus)

Abstract

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
Volume350
Issue number1
DOIs
Publication statusPublished - 2009 Feb 1

Fingerprint

Nonsmooth Domains
Sobolev spaces
Partial differential equations
Parabolic Equation
Derivatives
Hardy Inequality
Weighted Sobolev Spaces
Existence and Uniqueness Results
Parabolic Partial Differential Equations
Coefficient
Fractional
Non-negative
Derivative
Zero
Estimate

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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abstract = "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 H{\"o}lder 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.",
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AB - 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.

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KW - Unbounded leading coefficients

KW - Weighted Sobolev spaces

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