Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-18T13:41:36.343Z Has data issue: false hasContentIssue false
  • English
  • Français

The uniqueness of positive solutions of parabolic equations of divergence form on an unbounded domain

Published online by Cambridge University Press:  22 January 2016

Masaharu Nishio
Masaharu Nishio*
Affiliation:
Department of Mathematics, Osaka City University, Sugimoto, Sumiyoshi Osaka 558, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let Rn+1 = Rn × R be the (n + 1)-dimensional Euclidean space (n ≥ 1). For X ∈ Rn+1, we write X = (x, t) with x ∈ Rn and t ∈ R. We consider parabolic operators of the following form:

(1)

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 130 , June 1993 , pp. 111 - 121
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

References

[1] Aronson, D.G., Non-negative solutions of linear parabolic equations, Ann. Scuola Norm. Sup. Pisa, 22 (1968), 607–694.Google Scholar
[2] Fabes, E.B., Garofalo, N. and Salsa, S., A backward Harnack inequality and Fatou theorem for nonnnegative solutions of parabolic equations, Illinois J. Math., 30 (1986), 536–565.Google Scholar
[3] Kemper, J. T., Temperatures in several variables: kernel functions, representations, and parabolic boundary values, Trans. Amer. Math. Soc, 167 (1972), 243–262.Google Scholar
[4] Moser, J., A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math., 17 (1964), 101–134.Google Scholar