The classes Bm,1 and Hölder continuity for doubly degenerate parabolic equations

Abstract

Inner and boundary Hölder estimates for nonnegative weak solutions of quasilinear doubly degenerate parabolic equations are established. The proof of these results is based on studing some classes Bm,1 that can be considered as extensions of the classes B2 introduced by Ladyzhenskaya and Uraltseva and the classes Bm introduced by DiBenedetto. The embedding of the classes Bm,1 in appropriate Hölder spaces is proved. Bibliography: 20 titles.