Intrinsic Harnack estimates for nonnegative local solutions of degenerate parabolic equations

Abstract

We establish the intrinsic Harnack inequality for nonnegative solutions of the parabolic p p -Laplacian equation by a proof that uses neither the comparison principle nor explicit self-similar solutions. The significance is that the proof applies to quasilinear p p -Laplacian-type equations, thereby solving a long-standing problem in the theory of degenerate parabolic equations.