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Mat. Sb., 2019, Volume 210, Number 1, Pages 155–174 (Mi msb9019)  

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

S. E. Pastukhovaa, D. A. Yakubovichb

a 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.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 1.3270.2017/4.6
This research was supported by the Ministry of Education and Science of the Russian Federation (project no. 1.3270.2017/4.6).


DOI: https://doi.org/10.4213/sm9019

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

Bibliographic databases:

Document Type: Article
UDC: 517.956.25+517.956.8
MSC: 35J92
Received: 16.10.2017 and 19.05.2018

Citation: S. E. Pastukhova, D. A. Yakubovich, “Galerkin approximations for the Dirichlet problem with the $p(x)$-Laplacian”, Mat. Sb., 210:1 (2019), 155–174; Sb. Math., 210:1 (2019), 145–164

Citation in format AMSBIB
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