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Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations
Posted on 2010-03-16
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More E. B. Dynkin, "" 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. Contents: Introduction Analytic approach Probabilistic approach ℕ-measures Moments and absolute continuity properties of superdiffusions Poisson capacities Basic inequality Solutions w_Γ are σ-moderate All solutions are σ-moderate Appendix A: An elementary property of the Brownian motion Appendix B: Relations between Poisson and Bessel capacities References Subject index Notation index Not all books on / appear on the homepage. In order not to miss many of them follow Download Link (Ebooks section) (see top of each page on AH) and visit too :)
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