On the doubly singular equation g(u)t= Dpu

• Author(s): Henriques, Eurica ; Urbano, José Miguel
• Date: 2004
• Persistent ID: http://hdl.handle.net/10316/11421
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Doubly singular PDE; Regularity theory; Intrinsic scaling; Phase transition
• Document Type: Preprint
• Language: English

Description

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. CMUC/FCT; Project POCTI/34471/MAT/2000