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Superdiffusions and positive solutions of nonlinear partial differential equations

Author: E B Dynkin
Publisher: Providence, R.I. : American Mathematical Society, ©2004.
Series: University lecture series (Providence, R.I.), 34.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"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  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: E B Dynkin
ISBN: 082183682X 9780821836828 0821836048 9780821836040
OCLC Number: 55887441
Description: vi, 120 pages ; 26 cm.
Contents: Ch. 1. Introduction --
Ch. 2. Analytic approach --
Ch. 3. Probabilistic approach --
Ch. 4. N-measures --
Ch. 5. Moments and absolute continuity properties of superdiffusions --
Ch. 6. Poisson capacities --
Ch. 7. Basic inequality --
Ch. 8. Solutions [omega][tau] are [sigma]-moderate --
Ch. 9. All solutions are [sigma]-moderate --
App. A. An elementary property of the Brownian motion / J.-F. Le Gall --
App. B. Relations between Poisson and Bessel capacities / I.E. Verbitsky.
Series Title: University lecture series (Providence, R.I.), 34.
Responsibility: E.B. Dynkin.

Abstract:

Focuses on the applications of probability theory to the theory of nonlinear partial differential equations. This book is suitable for graduate students and research mathematicians interested in  Read more...

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