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Regularity of free boundaries in obstacle-type problems

Author: Arshak Petrosyan; Henrik Shahgholian; N N Uralʹt︠s︡eva
Publisher: Providence, R.I. : American Mathematical Society, ©2012.
Series: Graduate studies in mathematics, v. 136.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"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  Read more...
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Document Type: Book
All Authors / Contributors: Arshak Petrosyan; Henrik Shahgholian; N N Uralʹt︠s︡eva
ISBN: 9780821887943 0821887947
OCLC Number: 786273139
Description: x, 221 pages : illustrations ; 26 cm.
Contents: Model problems --
Optimal regularity of solutions --
Preliminary analysis of the free boundary --
Regularity of the free boundary : first results --
Global solutions --
Regularity of the free boundary : uniform results --
The singular set --
Touch with the fixed boundary --
The thin obstacle problem.
Series Title: Graduate studies in mathematics, v. 136.
Responsibility: Arshak Petrosyan, Henrik Shahgholian, Nina Uraltseva.

Abstract:

"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, $C1̂$, 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." -- amazon.com.

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