Intrinsic Harnack estimates for some doubly nonlinear degenerate parabolic equations. (English) Zbl 1160.35039
The authors prove an intrinsic Harnack inequality for non-negative local weak solutions for a class of doubly nonlinear degenerate parabolic equations, which include the standard pourous media equation and the parabolic \(p\)-Laplacian. The proof is based on measure-theoretical arguments and the Harnack inequality permits to establish the locally Hölder continuity of the solutions.
Reviewer: Elvira Mascolo (Firenze)
MSC:
35K65 | Degenerate parabolic equations |
35B65 | Smoothness and regularity of solutions to PDEs |
35B45 | A priori estimates in context of PDEs |
35K55 | Nonlinear parabolic equations |