Sharp numerical inclusion of the best constant for embedding on bounded convex domain

详细信息    查看全文

• 作者：Kazuaki Tanaka^a ; ^{imahazimari@fuji.waseda.jp" class="auth_mail" title="E-mail the corresponding author} ; Kouta Sekine^b ; Makoto Mizuguchi^a ; Shin&rsquo ; ichi Oishi^b
• 关键词：Computer-assisted proof ; Elliptic problem ; Embedding constant ; Error bounds ; Sobolev inequality ; Verified numerical computation
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：306-313
• 全文大小：820 K

文摘

In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding $H_0^1\left(\Omega \right)\hookrightarrow L^p\left(\Omega \right)$ on a bounded convex domain in R²${\mathbb{R}}^2$. 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.