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Regularity of Free Boundaries in Obstacle-Type Problems

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Regularity of Free Boundaries in Obstacle-Type Problems

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.
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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.
Produktdetaljer
Sprog: Engelsk
Sider: 221
ISBN-13: 9780821887943
Indbinding: Hardback
Udgave:
ISBN-10: 0821887947
Udg. Dato: 30 aug 2012
Længde: 0mm
Bredde: 0mm
Højde: 0mm
Forlag: American Mathematical Society
Oplagsdato: 30 aug 2012
Forfatter(e) Nina Uraltseva, Arshak Petrosyan, Henrik Shahgholian


Kategori Regning og matematisk analyse


Sprog Engelsk


Indbinding Hardback


Sider 221


Udgave


Længde 0mm


Bredde 0mm


Højde 0mm


Udg. Dato 30 aug 2012


Oplagsdato 30 aug 2012

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