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Regularity of Free Boundaries in Obstacle-Type Problems

Arshak Petrosyan | Henrik Shahgholian | Nina Uraltseva
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A01=Arshak Petrosyan
A01=Henrik Shahgholian
A01=Nina Uraltseva
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Author_Arshak Petrosyan
Author_Henrik Shahgholian
Author_Nina Uraltseva
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Product details

  • ISBN 9780821887943
  • Weight: 555g
  • Publication Date: 30 Aug 2012
  • Publisher: American Mathematical Society
  • Publication City/Country: US
  • Product Form: Hardback
  • Language: English
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Description
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.
About Arshak Petrosyan | Henrik Shahgholian | Nina Uraltseva
Arshak Petrosyan, Purdue University, West Lafayette, IN, USA

Henrik Shahgholian, Royal Institute of Technology, Stockholm, Sweden

Nina Uraltseva, St. Petersburg University, St. Petersburg, Russia

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