Galerkin approximations for the Dirichlet problem with the $p(x)$-Laplacian

S. E. Pastukhova   ; D. A. Yakubovich

Sbornik. Mathematics, Tome 210 (2019) no. 1, pp. 145-164

Résumé

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.

Détail

Keywords: Galerkin approximants, equations with variable order of nonlinearity, approximation error estimate.

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