**Graduate Studies in Mathematics**

Volume: 136;
2012;
221 pp;
Hardcover

MSC: Primary 35;

Print ISBN: 978-0-8218-8794-3

Product Code: GSM/136

List Price: $54.00

Individual Member Price: $43.20

**Electronic ISBN: 978-0-8218-8991-6
Product Code: GSM/136.E**

List Price: $54.00

Individual Member Price: $43.20

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#### Supplemental Materials

# Regularity of Free Boundaries in Obstacle-Type Problems

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*Arshak Petrosyan; Henrik Shahgholian; Nina Uraltseva*

The regularity theory of free boundaries flourished during the late 1970s and early 1980s and had a major impact in several areas of mathematics, mathematical physics, and industrial mathematics, as well as in applications. Since then the theory continued to evolve. Numerous new ideas, techniques, and methods have been developed, and challenging new problems in applications have arisen. The main intention of the authors of this book is to give a coherent introduction to the study of the regularity properties of free boundaries for a particular type of problems, known as obstacle-type problems. The emphasis is on the methods developed in the past two decades. The topics include optimal regularity, nondegeneracy, rescalings and blowups, classification of global solutions, several types of monotonicity formulas, Lipschitz, \(C^1\), as well as higher regularity of the free boundary, structure of the singular set, touch of the free and fixed boundaries, and more.

The book is based on lecture notes for the courses and mini-courses given by the authors at various locations and should be accessible to advanced graduate students and researchers in analysis and partial differential equations.

#### Table of Contents

# Table of Contents

## Regularity of Free Boundaries in Obstacle-Type Problems

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface ix10 free
- Introduction 112 free
- Chapter 1. Model problems 718 free
- Chapter 2. Optimal regularity of solutions 2940
- Chapter 3. Preliminary analysis of the free boundary 5768
- Chapter 4. Regularity of the free boundary: first results 8192
- Chapter 5. Global solutions 99110
- Chapter 6. Regularity of the free boundary: uniform results 115126
- Chapter 7. The singular set 133144
- Chapter 8. Touch with the fixed boundary 153164
- Chapter 9. The thin obstacle problem 167178
- Bibliography 201212
- Notation 211222
- Index 217228 free
- Back Cover Back Cover1233

#### Readership

Research mathematicians interested in partial differential equations, in particular in problems with free boundaries.