Softcover ISBN:  9780821836828 
Product Code:  ULECT/34 
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eBook ISBN:  9781470421793 
Product Code:  ULECT/34.E 
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AMS Member Price:  $52.00 
Softcover ISBN:  9780821836828 
eBook: ISBN:  9781470421793 
Product Code:  ULECT/34.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 
Softcover ISBN:  9780821836828 
Product Code:  ULECT/34 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470421793 
Product Code:  ULECT/34.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9780821836828 
eBook ISBN:  9781470421793 
Product Code:  ULECT/34.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 

Book DetailsUniversity Lecture SeriesVolume: 34; 2004; 120 ppMSC: Primary 60; Secondary 31; 35
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.
ReadershipGraduate students and research mathematicians interested in probability theory and its applications to differential equations.

Table of Contents

Chapters

Chapter 1. Introduction

Chapter 2. Analytic approach

Chapter 3. Probabilistic approach

Chapter 4. $\mathbb {N}$measures

Chapter 5. Moments and absolute continuity properties of superdiffusions

Chapter 6. Poisson capacities

Chapter 7. Basic inequality

Chapter 8. Solutions $w_\Gamma $ are $\sigma $moderate

Chapter 9. All solutions are $\sigma $moderate

Appendix A. An elementary property of the Brownian motion

Appendix B. Relations between Poisson and Bessel capacities


Additional Material

Reviews

This book is written by a wellknown specialist in the theory of Markov processes and partial differential equation...
Newsletter of the EMS


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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.
Graduate students and research mathematicians interested in probability theory and its applications to differential equations.

Chapters

Chapter 1. Introduction

Chapter 2. Analytic approach

Chapter 3. Probabilistic approach

Chapter 4. $\mathbb {N}$measures

Chapter 5. Moments and absolute continuity properties of superdiffusions

Chapter 6. Poisson capacities

Chapter 7. Basic inequality

Chapter 8. Solutions $w_\Gamma $ are $\sigma $moderate

Chapter 9. All solutions are $\sigma $moderate

Appendix A. An elementary property of the Brownian motion

Appendix B. Relations between Poisson and Bessel capacities

This book is written by a wellknown specialist in the theory of Markov processes and partial differential equation...
Newsletter of the EMS