TY - JOUR
T1 - Heat equation with a singular potential on the boundary and the Kato inequality
AU - Ishige, Kazuhiro
AU - Ishiwata, Michinori
PY - 2012/10
Y1 - 2012/10
N2 - 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.
AB - 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.
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U2 - 10.1007/s11854-012-0032-4
DO - 10.1007/s11854-012-0032-4
M3 - Article
AN - SCOPUS:84869051841
VL - 118
SP - 161
EP - 176
JO - Journal d'Analyse Mathematique
JF - Journal d'Analyse Mathematique
SN - 0021-7670
IS - 1
ER -