On the sobolev space theory of parabolic and elliptic equations in C 1 domains

Kyeong Hun Kim, N. V. Krylov

Research output: Contribution to journalArticlepeer-review

50 Scopus citations

Abstract

Existence and uniqueness results are given for second-order parabolic and elliptic equations with variable coefficients in C 1 domains in Sobolev spaces with weights allowing the derivatives of solutions to blow up near the boundary. The "number" of derivatives can be negative and fractional. The coefficients of parabolic equations are only assumed to be measurable in time.

Original languageEnglish (US)
Pages (from-to)618-642
Number of pages25
JournalSIAM Journal on Mathematical Analysis
Volume36
Issue number2
DOIs
StatePublished - 2005

Keywords

  • C domains
  • Parabolic equations
  • Sobolev spaces with weights

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