Existence of Lipschitz continuous solutions to the Cauchy–Dirichlet problem for anisotropic parabolic equations

Alkis S. Tersenov, Aris S. Tersenov

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

The Cauchy–Dirichlet and the Cauchy problem for the degenerate and singular quasilinear anisotropic parabolic equations are considered. We show that the time derivative ut of a solution u belongs to L under a suitable assumption on the smoothness of the initial data. Moreover, if the domain satisfies some additional geometric restrictions, then the spatial derivatives uxi belong to L as well. In the singular case we show that the second derivatives uxixj of a solution of the Cauchy problem belong to L2.

Original languageEnglish
Pages (from-to)3965-3986
Number of pages22
JournalJournal of Functional Analysis
Volume272
Issue number10
DOIs
Publication statusPublished - 15 May 2017

Keywords

  • Degenerate parabolic equations
  • Singular parabolic equations
  • DEGENERATE
  • ULTRAPARABOLIC EQUATION

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