On the doubly singular equation g(u)t= Dpu
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...
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| Formato: | other |
| Idioma: | eng |
| Publicado em: |
2004
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| Texto completo: | http://hdl.handle.net/10316/11421 |
| País: | Portugal |
| Oai: | oai:estudogeral.sib.uc.pt:10316/11421 |
| Resumo: | 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 di usion. |
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