有界凸区域上嵌入$H_{0}^{1}(Ω) \hookrightarrow L^{p}(Ω)$的最佳常数的精确数值包含
Sharp numerical inclusion of the best constant for embedding $H_{0}^{1}(Ω) \hookrightarrow L^{p}(Ω)$ on bounded convex domain
摘要：
本文提出了一种数值方法，用于在$\mathbb{R}^{2}$中获得嵌入$H_{0}^{1}(Ω) \hookrightarrow L^{p}(Ω)$在有界凸区域上的最佳常数的精确包含。我们估计的最佳常数计算相应的极值函数使用验证数值计算。验证数值包含的最佳常数的平方域。
英文摘要：
In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding $H_{0}^{1}(Ω) \hookrightarrow L^{p}(Ω)$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
