Regularity in Sobolev spaces for doubly nonlinear parabolic equations

The doubly nonlinear parabolic equation ut=div[ (um−1u)p−2 (um−1u)] (m>1,m(p−1)>1)is considered in several dimensions and regularity results in fractional order Sobolev spaces are obtained. The main tools in the proof are a difference quotient technique and the imbedding theorem of Nikolskii spaces into Sobolev spaces.