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 language | English (US) |
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Pages (from-to) | 919-955 |
Number of pages | 37 |
Journal | Communications in Partial Differential Equations |
Volume | 30 |
Issue number | 4-6 |
DOIs | |
State | Published - Aug 18 2005 |
Externally published | Yes |
Bibliographical note
Generated from Scopus record by KAUST IRTS on 2023-02-15ASJC Scopus subject areas
- Analysis
- Applied Mathematics