Sharp numerical inclusion of the best constant for embedding $H_0^1(\Omega )\hookrightarrow L^p(\Omega )$ on bounded convex domain

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.

12 pages, 1 figure

References in corpus (1)

• A numerical investigation of level sets of extremal Sobolev functions

Cited by in corpus (2)

• Numerical verification method for positive solutions of elliptic problems
• A posteriori verification for the sign-change structure of solutions of elliptic partial differential equations