Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations

Released on by Evgeniĭ Borisovich Dynkin
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  • Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations Book Detail

  • Author : Evgeniĭ Borisovich Dynkin
  • Release Date : 2004
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 130
  • ISBN 13 : 082183682X
  • File Size : 16,16 MB
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Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations by Evgeniĭ Borisovich Dynkin PDF Summary

Book Description: 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.

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