Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-17T10:19:52.120Z Has data issue: false hasContentIssue false
  • English
  • Français

Construction of fundamental solutions of hypoelliptic equations by the use of a probabilistic method

Published online by Cambridge University Press:  22 January 2016

T. Matsuzawa
T. Matsuzawa*
Affiliation:
Department of Mathematics, Nagoya University
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.

A. Friedman, [5] has constructed the fundamental solutions for a class of degenerate parabolic equations of the second order by making use of a probabilistic method and obtained the estimates for the fundamental solutions, especially near the degenerating manifolds (obstacles) of given operators, where a probabilistic method plays an important role.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 72 , December 1978 , pp. 103 - 126
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

References

[1] Bony, J.-M., Principe du maximum. Inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés, Ann. Inst. Fourier, Grenoble 19(1) (1969), 277’304.Google Scholar
[2] Freidlin, M. I., On the factorization of nonnegative definite matrices, Theor. Pro bability Appl. 13 (1968), 354’356.CrossRefGoogle Scholar
[3] Friedman, A., Partial differential equations of parabolic type, Prentice-Hall (1964).Google Scholar
[4] Freidlin, , Stochastic differential equations and applications, Vol. 1, 2, Academic Press(1975).Google Scholar
[5] Freidlin, , Fundamental solutions for degenerate parabolic equations, Acta Math. 133(1974), 171’217.Google Scholar
[6] Ichihara, K. and Kunita, H., A classification of the second order degenerate elliptic operators and its probabilistic characterization, Z. Wahrscheinlichkeitstheorieverw. Gebiete 30 (1974), 235’254.Google Scholar
[7] Matsuzawa, T., On some degenerate parabolic equations I, Nagoya Math. J. 51(1973), 57’77, II, Nagoya Math. J. 52 (1973), 61’84.Google Scholar
[8] Oleinik, O. A., Alcuni risultati sulle equazioni lineari elliptico-paraboliche a derivate parziali del secondo ordine, Rend. Classe, Sci. Fis. Mat. Nat. Acad. Naz. Lin cei, Ser. 8, Vol., 40 (1966), 775’784.Google Scholar
[9] Oleinik, 0. A. and Radkevich, E. V., Second order equations with nonnegative chara cteristic form, American Math. Soc., Providence, 1973.Google Scholar
[10] Schwartz, L., Théorie des noyaux, Proc. International Congress of Mathematicians, Vol. 1, 220’230, American Math. Soc. Providence, 1952.Google Scholar
[11] Strook, D. and Varadhan, S. R. S., On degenerate elliptic-parabolic operators of second order and their associated diffusions, Comm. Pure Applied Math., Vol. 25 (1972), 651’713.Google Scholar