Regularity in Sobolev spaces for doubly nonlinear parabolic equations

The doubly nonlinear parabolic equation u t = div [| ∇ (|u| m−1 u)| p−2 ∇ (|u| m−1 u)] (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.