A regularity theory for a more general class of quasilinear parabolic partial differential equations and variational inequalities

Hi Jun Choe, James Serrin

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8 Citations (Scopus)

Abstract

By means of an inequality of Poincaré type, a weak Harnack inequality for the gradient of a solution and an integral inequality of Campanato type, it is shown that solutions to degenerate parabolic variational inequalities are locally Hölder continuous. Using a difference quotient method and Moser type iteration it is then proved that the gradient of a solution is locally bounded. Finally using iteration and scaling it is shown that the gradient of the solution satisfies a Campanato type integral inequality and is locally Hölder continuous.

Original languageEnglish
Pages (from-to)915-944
Number of pages30
JournalDifferential and Integral Equations
Volume5
Issue number4
Publication statusPublished - 1992 Jul

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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