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

Kazuhiro Ishige; Michinori Ishiwata

doi:10.1007/s11854-012-0032-4

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

Kazuhiro Ishige, Michinori Ishiwata

SCI - Mathematics

Research output: Contribution to journal › Article

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 language	English
Pages (from-to)	161-176
Number of pages	16
Journal	Journal d'Analyse Mathematique
Volume	118
Issue number	1
DOIs	https://doi.org/10.1007/s11854-012-0032-4
Publication status	Published - 2012 Oct 1

ASJC Scopus subject areas

Analysis
Mathematics(all)

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Ishige, K., & Ishiwata, M. (2012). Heat equation with a singular potential on the boundary and the Kato inequality. Journal d'Analyse Mathematique, 118(1), 161-176. https://doi.org/10.1007/s11854-012-0032-4

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