On the doubly singular equation y(u)t = Δpu

Eurica Henriques, José Miguel Urbano

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We prove that local weak solutions of a nonlinear parabolic equation with a doubly singular character are locally continuous. One singularity occurs in the time derivative and is due to the presence of a maximal monotone graph; the other comes up in the principal part of the PDE, where the p-Laplace operator is considered. The paper extends to the singular case 1 < p < 2, the results obtained previously by the second author for the degenerate case p > 2; it completes a regularity theory for a type of PDEs that model phase transitions for a material obeying a nonlinear law of diffusion. Copyright © Taylor & Francis, Inc.
Original languageEnglish (US)
Pages (from-to)919-955
Number of pages37
JournalCommunications in Partial Differential Equations
Volume30
Issue number4-6
DOIs
StatePublished - Aug 18 2005
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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