Cover of E. B Dynkin: Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations

E. B Dynkin Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations

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American Mathematical Society

2015

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978-1-4704-2179-3

1-4704-2179-8

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This book is devoted to the applications of probability theory to the theory of nonlinear partial differential equations. More precisely, it is shown that all positive solutions for a class of nonlinear elliptic equations in a domain are described in terms of their traces on the boundary of the domain. The main probabilistic tool is the theory of superdiffusions, which describes a random evolution of a cloud of particles. A substantial enhancement of this theory is presented that can be of interest for everybody who works on applications of probabilistic methods to mathematical analysis.

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