Hölder Continuity of Solutions to Nonlinear Parabolic Equations Degenerated on a Part of the Domain

详细

We study the regularity of solutions to parabolic p-Laplace type equations degenerating uniformly with respect to a small parameter ε on a part of the domain. We prove ε-uniform estimates for the maximum of modulus, and Hölder estimates for the modulus of continuity of the solution. We also prove the Harnack inequality of a special form.