A geometric tangential approach to sharp regularity for degenerate evolution equations

Eduardo V. Teixeira, José Miguel Urbano

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

That the weak solutions of degenerate parabolic PDEs modelled on the inhomogeneous p-Laplace equation ut-div(|∇u|p-2∇u)= f ∈ Lq,r, p≥2 are C0,α for some α ∈ (0,1) has been known for almost 30 years. What was hitherto missing from the literature was a precise and sharp knowledge of the Hölder exponent α in terms of p, q, r and the space dimension n. We show in this paper that using a method based on the notion of geometric tangential equations and the intrinsic scaling of the p-parabolic operator. The proofs are flexible enough to be of use in a number of other nonlinear evolution problems. © 2014 Mathematical Sciences Publishers.
Original languageEnglish (US)
Pages (from-to)733-744
Number of pages12
JournalAnalysis and PDE
Volume7
Issue number3
DOIs
StatePublished - Jan 1 2014
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

  • Numerical Analysis
  • Analysis
  • Applied Mathematics

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