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arXiv · 1503.05468

Sharp numerical inclusion of the best constant for embedding $H_{0}^{1}(\Omega) \hookrightarrow L^{p}(\Omega)$ on bounded convex domain

Kazuaki Tanaka·Kouta Sekine·Makoto Mizuguchi·Shin'ichi Oishi
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Abstract

In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding $H_{0}^{1}(\Omega) \hookrightarrow L^{p}(\Omega)$ on bounded convex domain in $\mathbb{R}^{2}$. We estimate the best constant by computing the corresponding extremal function using a verified numerical computation. Verified numerical inclusions of the best constant on a square domain are presented.

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Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, Shin'ichi Oishi. 2015-03-18. Sharp numerical inclusion of the best constant for embedding $H_{0}^{1}(\Omega) \hookrightarrow L^{p}(\Omega)$ on bounded convex domain. https://doi.org/10.1016/j.cam.2016.07.021

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