This article is cited in 3 papers

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

S. E. Pastukhova^a, D. A. Yakubovich<sup>b

a</sup> MIREA — Russian Technological University, Moscow, Russia
^b Vladimir State University named after Alexander and Nikolay Stoletovs, Vladimir, Russia

Abstract: 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.

UDC: 517.956.25+517.956.8

MSC: 35J92

Received: 16.10.2017 and 19.05.2018

DOI: 10.4213/sm9019

 English version: Sbornik: Mathematics, 2019, 210:1, 145–164

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