Quasilinear two-phase Venttsel problems

A majorant of the Hölder norms is established for solutions of the two-phase quasilinear parabolic (elliptic) boundary value problems with degenerate and nondegenerate Venttsel interface conditions. In addition, gradient estimates for solutions of the two-phase quasilinear nondegenerate Venttsel problems as well as the solvability results in Sobolev and Hölder spaces are obtained.