**University Lecture Series**

Volume: 34;
2004;
120 pp;
Softcover

MSC: Primary 60;
Secondary 31; 35

Print ISBN: 978-0-8218-3682-8

Product Code: ULECT/34

List Price: $34.00

Individual Member Price: $27.20

**Electronic ISBN: 978-1-4704-2179-3
Product Code: ULECT/34.E**

List Price: $34.00

Individual Member Price: $27.20

#### Supplemental Materials

# Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations

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*E. B. Dynkin*

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.

#### Readership

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

#### Reviews & Endorsements

This book is written by a well-known specialist in the theory of Markov processes and partial differential equation...

-- Newsletter of the EMS

#### Table of Contents

# Table of Contents

## Superdiffusions and Positive Solutions of Nonlinear Partial Differential Equations

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents iii4 free
- Preface v6 free
- Chapter 1. Introduction 18 free
- Chapter 2. Analytic approach 916
- Chapter 3. Probabilistic approach 1926
- Chapter 4. N-measures 3542
- Chapter 5. Moments and absolute continuity properties of superdiffusions 4956
- Chapter 6. Poisson capacities 6168
- Chapter 7. Basic inequality 7178
- Chapter 8. Solutions wp are a- moderate 7986
- Chapter 9. All solutions are σ-moderate 8996
- Appendix A. An elementary property of the Brownian motion 103110
- Appendix B. Relations between Poisson and Bessel capacities 107114
- References 113120
- Subject Index 117124
- Notation Index 119126
- Back Cover Back Cover1130