Geodesic
Galerkin approximations for the Dirichlet problem with the $p(x)$-Laplacian
Sbornik. Mathematics, Tome 210 (2019) no. 1, pp. 145-164

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We study the Dirichlet problem with $p(\,\cdot\,)$-Laplacian in a bounded domain, where $p(\,\cdot\,)$ is a measurable function whose range is bounded away from $1$ and $\infty$. A system of Galerkin approximations is constructed for the so-called $H$-solution or any other variational solution, and energy norm error estimates are proved. References: 19 items.
Keywords: Galerkin approximants, equations with variable order of nonlinearity, approximation error estimate. 
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     author = {S. E. Pastukhova and D. A. Yakubovich},
     title = {Galerkin approximations for the {Dirichlet} problem with the $p(x)${-Laplacian}},
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S. E. Pastukhova; D. A. Yakubovich. Galerkin approximations for the Dirichlet problem with the $p(x)$-Laplacian. Sbornik. Mathematics, Tome 210 (2019) no. 1, pp. 145-164. http://geodesic.mathdoc.fr/item/SM_2019_210_1_a4/