$H^2$ regularity for the $p(x)-$ Laplacian in two-dimensional convex domains

preprint2011arXivOpen access

In this paper we study the $H^2$ global regularity for solutions of the $p(x)-$ Laplacian in two dimensional convex domains with Dirichlet boundary conditions. Here $p:Ω\to [p_1,\infty)$ with $p\in Lip(\barΩ)$ and $p_1>1$ .

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$H^2$ regularity for the $p(x)-$ Laplacian in two-dimensional convex domains

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$H^2$ regularity for the $p(x)-$ Laplacian in two-dimensional convex domains