Existence and fractional regularity of solutions for a doubly nonlinear differential inclusion

This article considers the issues of existence and regularity of solutions to the following doubly nonlinear differential inclusion $$omega_t+alpha (omega_t)-Delta omega-Delta_p{omega} ni f$$ where α is a maximal monotone operator in ${mathbb{R}^2}$ and Δ _p denotes the p-Laplacian with p > 2. The investigation on fractional regularity is based on the Galerkin method combined with a suitable basis for W ^1,p , which we exhibit as a preliminary result. This approach also allows the obtaining of estimates in the so-called Nikolskii spaces, since it balances the interplay between the maximal monotone operator with the appearing higher order nonlinear terms.