Local Hölder continuity for doubly nonlinear parabolic equations

Tuomo Kuusi, Juhana Siljander, José Miguel Urbano

Research output: Contribution to journalArticleScientificpeer-review

12 Citations (Scopus)

Abstract

We give a proof of the Hölder continuity of weak solutions of certain degenerate doubly nonlinear parabolic equations in measure spaces. We only assume the measure to be a doubling nontrivial Borel measure which supports a Poincaré inequality. The proof discriminates between large scales, for which a Harnack inequality is used, and small scales, which require intrinsic scaling methods.

Original languageEnglish
Pages (from-to)399-430
Number of pages32
JournalIndiana University Mathematics Journal
Volume61
Issue number1
DOIs
Publication statusPublished - 2012
MoE publication typeA1 Journal article-refereed

Keywords

  • Caccioppoli estimates
  • Harnack's inequality
  • Hölder continuity
  • Intrinsic scaling

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