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

Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, Shin'ichi Oishi

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)306-313
Number of pages8
JournalJournal of Computational and Applied Mathematics
Publication statusPublished - 2017 Feb 1


  • Computer-assisted proof
  • Elliptic problem
  • Embedding constant
  • Error bounds
  • Sobolev inequality
  • Verified numerical computation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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