Regularity of Free Boundaries in Obstacle-Type Problems

Arshak Petrosyan, Henrik Shahgholian, Nina Uraltseva (Autoren)

Buch | Hardcover

221 Seiten

2012
American Mathematical Society (Verlag)
978-0-8218-8794-3 (ISBN)

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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.

Arshak Petrosyan, Purdue University, West Lafayette, IN, USA Henrik Shahgholian, Royal Institute of Technology, Stockholm, Sweden Nina Uraltseva, St. Petersburg University, St. Petersburg, Russia

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
Bibliography
Notation
Index

Erscheint lt. Verlag	28.5.2013
Reihe/Serie	Graduate Studies in Mathematics
Verlagsort	Providence
Sprache	englisch
Gewicht	555 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	0-8218-8794-7 / 0821887947
ISBN-13	978-0-8218-8794-3 / 9780821887943
Zustand	Neuware