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Book Information

Author(s): E. B. Dynkin
Title: Diffusions, superdiffusions and partial differential equations
Additional book information: Colloquium Publications, vol. 50, American Mathematical Society, Providence, RI, 2002, xi + 236, $49.00, 0-8218-3174-7

1.: M. Brélot, Éléments de la théorie classique du potentiel, Les cours de Sorbonne, Centre de Documentation Universitaire, Paris V, 1959. MR 21:5099
2.: R. K. Courant, K. Friedrichs and H. Lewy, Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 100 (1928), 32-74.
3.: D. A. Dawson, Measure-valued Markov processes, in École d'Été de Probabilités de Saint Flour XXI, Lecture Notes in Mathematics 1541, Springer-Verlag, 1993, 1-261. MR 94m:60101
4.: D. A. Dawson and K. Fleischmann, Catalytic and mutually catalytic branching, in Infinite Dimensional Stochastic Analysis, eds. Ph. Clément, F. den Hollander, J. van Neerven and B. de Pagter, Royal Netherlands Academy, Amsterdam, 145-170, 2000. MR 2002f:60164
5.: J. L. Doob, Classical potential theory and its probabilistic counterpart, Springer, 1984. MR 85k:31001
6.: E. B. Dynkin, Markov Processes, I, II, Springer-Verlag, 1965. MR 33:1887
7.: E. B. Dynkin, A probabilistic approach to one class of nonlinear differential equations, Probab. Th. Rel. Fields 89 (1991), 89-115. MR 92d:35090
8.: E. B. Dynkin, An introduction to branching measure-valued processes, CRM Monograph Series, vol. 6, AMS, 1994. MR 96f:60145
9.: E. B. Dynkin, A new inequality for superdiffusions and its applications to nonlinear differential equations, manuscript, 2003.
10.: E. B. Dynkin, Superdiffusions and positive solutions of nonlinear partial differential equations, to appear in Uspekhi Mat. Nauk., 2003.
11.: E. B. Dynkin and S. E. Kuznetsov, Superdiffusions and removable singularities for quasilinear partial differential equations, Comm. Pure Appl. Math. 49 (1996), 125-176. MR 97m:60114
12.: G. Hunt, Markov processes and potentials I, II, III, Illinois J. Math. 1 (1957), 44-93; 1 (1957), 316-369; 2 (1958), 151-213. MR 19:951g, MR 21:5824
13.: I. Iscoe, On the supports of measure-valued critical branching Brownian motions, Ann. Probab. 16 (1988), 200-221. MR 88j:60097
14.: S. Kakutani, Two dimensional Brownian moion and harmonic functions, Proc. Imp. Acad. Tokyo 20 (1944), 227-233. MR 7:315b
15.: S. Kakutani, Markov processes and the Dirichlet problem, Proc. Imp. Acad. Tokyo 21, 227-233, 1945. MR 11:357h
16.: J.-F. Le Gall, A probabilistic Poisson representation for positive solutions $\Delta u=u^2$ in a planar domain, Comm. Pure Appl. Math. 50 (1997), 69-103. MR 98c:60144
17.: J.-F. Le Gall, Spatial branching processes, random snakes and partial differential equations, Birkhäuser, 1999. MR 2001g:60211
18.: J.-F. Le Gall and L. Mytnik, Regularity and irregularity of the exit measure density for $(1+\beta)$ stable super-Brownian motion, 2003 preprint.
19.: R. S. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc. 49 (1941), 137-172. MR 2:292h
20.: M. B. Mselati, Classification et répresentation probabiliste des solutions positives de $\Delta u=u^{2}$ dans un domaine, Thèse Doctorat de l'Université Paris 6, 2002.
21.: M. B. Mselati, Classification et répresentation probabiliste des solutions positives d'une équation elliptique semi-linéaire, C. R. Acad. Sci. Paris Ser. I 335, 733-738, 2002.
22.: M. Marcus and L. Véron, The boundary trace of positive solutions of semilinear elliptic equations, I. The subcritical case, Arch. Rat. Mech. Anal. 144 (1998), 201-231. MR 2000a:35077
23.: M. Marcus and L. Véron, Capacitary estimates of solutions of a class of nonlinear elliptic equations, C. R. Acad. Sci. Paris Ser. I 336, 2003.
24.: E. A. Perkins, Dawson-Watanabe Superprocesses and Measure-valued Diffusions, Ecole d'été de probabilités (Saint Flour, 1999), Lecture Notes in Math. 1781, Springer, 2002, 125-324. MR 2003k:60104
25.: H. B. Phillips and N. Wiener, Nets and Dirichlet problem, J. Math. Phys. 2, 105-124, 1923.
26.: G. Slade, Scaling limits and super-Brownian motion, Notices AMS, 49, 1056-1067, 2002. MR 2003g:60170
27.: L. Véron, Singularities of Solutions of Second Order Quasilinear Equations, Pitman Research Notes in Math. 353, Addison Wesley Longman Inc., 1966. MR 98b:35053
28.: L. Véron, Generalized boundary value problems for nonlinear elliptic equations, Electron. J. Diff. Equ. Conf. 6, 313-342, 2001. MR 2001j:35099
29.: S. Watanabe, A limit theorem on branching processes and continuous state branching processes, J. Math. Kyoto Univ. 8, 141-167, 2001. MR 38:5301
30.: N. Wiener, Differential space, J. Math Phys. 2, 131-174, 1923.

Reviewer(s):
Donald Dawson
Affiliation: Carleton University and McGill University
Email: ddawson@math.carleton.ca

MSC (2000): Primary 60J60, 35-XX; Secondary 35K55, 60J65
DOI: 10.1090/S0273-0979-04-01002-X
PII: S 0273-0979(04)01002-X
Posted: January 8, 2004
Copyright of article: Copyright 2004, American Mathematical Society

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