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.


35K65 Degenerate parabolic equations
35B65 Smoothness and regularity of solutions to PDEs
35B45 A priori estimates in context of PDEs
35K55 Nonlinear parabolic equations