Abstract
This article considers the issues of existence and regularity of solutions to the following doubly nonlinear differential inclusion
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.
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Boldrini, J.L., de Miranda, L.H. & Planas, G. Existence and fractional regularity of solutions for a doubly nonlinear differential inclusion. J. Evol. Equ. 13, 535–560 (2013). https://doi.org/10.1007/s00028-013-0189-z
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DOI: https://doi.org/10.1007/s00028-013-0189-z