Sharp numerical inclusion of the best constant for embedding H01(Ω)↪Lp(Ω) on bounded convex domain

摘要

In this paper, we propose a verified numerical method for obtaining a sharp inclusion of the best constant for the embedding H01(Ω)↪Lp(Ω) on a bounded convex domain in 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.