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.