Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations (University Lecture Series)

Dynkin's lecture on the application of probability theory to the theory of nonlinear partial differential equations shows that all positive solutions for a class on nonlinear elliptical equations in a domain are described in terms of their traces on the boundary of the domain. While here Dynkin's main problematic tool is the theory of superdiffusion, which describes the random evolution of a cloud of particles, his analytic and problematical approaches and observations would be of interest to those working on other applications of probability in mathematical analysis. Appendices include a description of an elementary property of the Brownian motion by Le Gall and an examination of the relations between Poisson and Bessel capacities by Verbitsky. Annotation ©2004 Book News, Inc., Portland, OR (booknews.com)