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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, and Nina Uraltseva, St. Petersburg University, Russia
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Graduate Studies in Mathematics
2012; 221 pp; hardcover
Volume: 136
ISBN-10: 0-8218-8794-7
ISBN-13: 978-0-8218-8794-3
List Price: US$54
Member Price: US$43.20
Order Code: GSM/136
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A Geometric Approach to Free Boundary Problems - Luis Caffarelli and Sandro Salsa

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.

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