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Superdiffusions and positive solutions of nonlinear partial differential equations

โœ Scribed by E. B. Dynkin

Publisher
Amer Mathematical Society
Year
2004
Tongue
English
Leaves
130
Series
University Lecture Series 034
Category
Library
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โœฆ Synopsis

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. Also of interest by this author is ""Diffusions, Superdiffusions and Partial Differential Equations"" in the ""AMS"" series, Colloquium Publications

๐Ÿ“œ SIMILAR VOLUMES

Superdiffusions and Positive Solutions o
๐Ÿ“ Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations
โœ E. B. Dynkin ๐Ÿ“‚ Library ๐Ÿ“… 2004 ๐Ÿ› American Mathematical Society ๐ŸŒ English

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 doma

Superdiffusions and positive solutions o
๐Ÿ“ Superdiffusions and positive solutions of nonlinear partial differential equations
โœ E. B. Dynkin ๐Ÿ“‚ Library ๐Ÿ“… 2004 ๐Ÿ› American Mathematical Society ๐ŸŒ English

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 doma

Diffusions, superdiffusions, and partial
๐Ÿ“ Diffusions, superdiffusions, and partial differential equations
โœ E. B. Dynkin ๐Ÿ“‚ Library ๐Ÿ“… 2002 ๐Ÿ› American Mathematical Society ๐ŸŒ English

Interactions between the theory of partial differential equations of elliptic and parabolic types and the theory of stochastic processes are beneficial for both probability theory and analysis. At the beginning, mostly analytic results were used by probabilists. More recently, analysts (and physicis