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Regularity of Free Boundaries in Obstacle-Type Problems
 
Arshak Petrosyan Purdue University, West Lafayette, IN
Henrik Shahgholian Royal Institute of Technology, Stockholm, Sweden
Nina Uraltseva St. Petersburg University, St. Petersburg, Russia
Regularity of Free Boundaries in Obstacle-Type Problems
Hardcover ISBN:  978-0-8218-8794-3
Product Code:  GSM/136
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-0-8218-8991-6
Product Code:  GSM/136.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-0-8218-8794-3
eBook: ISBN:  978-0-8218-8991-6
Product Code:  GSM/136.B
List Price: $184.00 $141.50
MAA Member Price: $165.60 $127.35
AMS Member Price: $147.20 $113.20
Regularity of Free Boundaries in Obstacle-Type Problems
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Regularity of Free Boundaries in Obstacle-Type Problems
Arshak Petrosyan Purdue University, West Lafayette, IN
Henrik Shahgholian Royal Institute of Technology, Stockholm, Sweden
Nina Uraltseva St. Petersburg University, St. Petersburg, Russia
Hardcover ISBN:  978-0-8218-8794-3
Product Code:  GSM/136
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-0-8218-8991-6
Product Code:  GSM/136.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-0-8218-8794-3
eBook ISBN:  978-0-8218-8991-6
Product Code:  GSM/136.B
List Price: $184.00 $141.50
MAA Member Price: $165.60 $127.35
AMS Member Price: $147.20 $113.20
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 1362012; 221 pp
    MSC: Primary 35;

    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.

    Readership

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

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Chapter 1. Model problems
    • Chapter 2. Optimal regularity of solutions
    • Chapter 3. Preliminary analysis of the free boundary
    • Chapter 4. Regularity of the free boundary: first results
    • Chapter 5. Global solutions
    • Chapter 6. Regularity of the free boundary: uniform results
    • Chapter 7. The singular set
    • Chapter 8. Touch with the fixed boundary
    • Chapter 9. The thin obstacle problem
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1362012; 221 pp
MSC: Primary 35;

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.

Readership

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

  • Chapters
  • Introduction
  • Chapter 1. Model problems
  • Chapter 2. Optimal regularity of solutions
  • Chapter 3. Preliminary analysis of the free boundary
  • Chapter 4. Regularity of the free boundary: first results
  • Chapter 5. Global solutions
  • Chapter 6. Regularity of the free boundary: uniform results
  • Chapter 7. The singular set
  • Chapter 8. Touch with the fixed boundary
  • Chapter 9. The thin obstacle problem
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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