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)|
|Number of pages||37|
|Journal||Communications in Partial Differential Equations|
|State||Published - Aug 18 2005|
Bibliographical noteGenerated from Scopus record by KAUST IRTS on 2023-02-15
ASJC Scopus subject areas
- Applied Mathematics