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This article is cited in 2 scientific papers (total in 2 papers)
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.
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
Linking options:
https://www.mathnet.ru/eng/sm9019https://doi.org/10.1070/SM9019 https://www.mathnet.ru/eng/sm/v210/i1/p155
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Abstract page: | 522 | Russian version PDF: | 46 | English version PDF: | 18 | References: | 48 | First page: | 39 |
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