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

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• 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 w the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716303405&_mathId=si26.gif&_user=111111111&_pii=S0377042716303405&_rdoc=1&_issn=03770427&md5=9cd7816ee27eeaf663ade6560d4c02d8">width="115" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0377042716303405-si26.gif"> on a bounded convex domain in w the MathML source">R². 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.