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)
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Paperback. Condizione: New. 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. Codice articolo LU-9780821836828
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Condizione: New. 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 probability theory and its applications to differential equations. Series: University Lecture Series. Num Pages: 120 pages. BIC Classification: PBKJ. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Weight in Grams: 244. . 2004. Mass Market Paperback. . . . . Books ship from the US and Ireland. Codice articolo V9780821836828
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Condizione: New. 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 probability theory and its applications to differential equations. Series: University Lecture Series. Num Pages: 120 pages. BIC Classification: PBKJ. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Weight in Grams: 244. . 2004. Mass Market Paperback. . . . . Codice articolo V9780821836828
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Paperback. Condizione: New. 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. Codice articolo LU-9780821836828
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