Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations - ISBN:082183682X

Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations

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E. B. Dynkin, "Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations"
American Mathematical Society | 2004 | ISBN: 082183682X | 120 pages | PDF | 1,2 MB
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 will be of interest to anyone who works on applications of probabilistic methods to mathematical analysis.
The book is suitable for graduate students and research mathematicians interested in probability theory and its applications to differential equations.

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