Heat equation with a singular potential on the boundary and the Kato inequality

Kazuhiro Ishige, Michinori Ishiwata

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This paper is concerned with the heat equation in the half-space ℝ + N with the singular potential function on the boundary, where N ≥ 3, ω > 0, 0 < T ≤ ∞, and u 0 ∈ C 0(ℝ + N). We prove the existence of a threshold number ω N for the existence and the nonexistence of positive solutions of (P), which is characterized as the best constant of the Kato inequality in ℝ + N.

Original languageEnglish
Pages (from-to)161-176
Number of pages16
JournalJournal d'Analyse Mathematique
Volume118
Issue number1
DOIs
Publication statusPublished - 2012 Oct 1

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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