Two-Phase Problem for Quasilinear Parabolic Systems with Nondiagonal Principal Matrix. Regularity of Weak Solutions

详细

We study the regularity of weak solutions to the two-phase the problem for quasilinear parabolic systems with nondiagonal principal matrices. We prove the Hölder continuity of solutions on a set of full measure with an estimate for the admissible singular set. For solutions to the corresponding linear problem we establish the Hölder continuity in a neighborhood of the medium interface.