Classification And Probabilistic Representation Of The Positive Solutions Of A Semilinear Elliptic Equation
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Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation
Author: Benoît Mselati
language: en
Publisher: American Mathematical Society(RI)
Release Date: 2014-09-11
An analytic approach to the equation $\Delta u = u^2$ A probabilistic approach to the equation $\Delta u = u^2$ Lower bounds for solutions Upper bounds for solutions The classification and representation of the solutions of $\Delta u = u^2$ in a domain Appendix A. Technical results Appendix. Bibliography Notation index Subject index.
Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation
Author: Benoît Mselati
language: en
Publisher: American Mathematical Soc.
Release Date: 2004
Concerned with the nonnegative solutions of $\Delta u = u^2$ in a bounded and smooth domain in $\mathbb{R}^d$, this title intends to prove that they are uniquely determined by their fine trace on the boundary as defined in [DK98a], answering a major open question of [Dy02].
Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations
Author: Evgeniĭ Borisovich Dynkin
language: en
Publisher: American Mathematical Soc.
Release Date: 2004
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.