Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-11T09:20:29.841Z Has data issue: false hasContentIssue false
  • English
  • Français

Poincaré type conditions of the regularity for the parabolic operator of order α

Published online by Cambridge University Press:  22 January 2016

Masayuki Itô  and
Masaharu Nishio
Masayuki Itô
Affiliation:
Department of Mathematics, College of General Education, Nagoya University, Chikusa-ku, Nagoya, 464, Japan
Masaharu Nishio
Affiliation:
Department of Mathematics, School of Sciences, Nagoya University, Chikusa-ku, Nagoya, 464, 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 denote the (n + 1)-dimensional Euclidean space (n ≧ 1). For X ∊ Rn+1 we write X = (x, t) with x ∊ Rn and t ∊ R. In this case, Rn is called the x-space of Rn+1 = Rn × R.

For an α with 0 < α < 1, we write

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 115 , September 1989 , pp. 1 - 22
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

[1] Berg, C. and Forst, G., Potential theory on locally compact abelian groups, Springer-Verlag, Berlin Heiderberg New York, 1975.Google Scholar
[2] Choquet, G. and Deny, J., Sur l’equation de convolution μ=μ*σ , C. R. Acad. Sci., 250 (1960), 799–801.Google Scholar
[3] Effros, E. and Kazdan, J., On the Dirichlet problem for the heat equation, Indiana U. Math. J., 20 (1971), 683–693.Google Scholar
[4] Elliot, J., Dirichlet spaces and integro-differential operators, Part I, Illinois J. Math., 9 (1965), 87–98.Google Scholar
[5] Evans, L. and Griepy, R., Wiener’s criterion for the heat equation, Arch. Rational Mech. Anal., 78 (1982), 293–314.Google Scholar
[6] Helms, L. L., Introduction to potential theory, Wiley-Interscience, New York, 1969.Google Scholar
[7] Herz, C. R., Analyse harmonique à plusiers variables, Sém. Math. d’Orsay, 1965/66.Google Scholar