Regularity of free boundaries in obstacle-type problems / Arshak Petrosyan, Henrik Shahgholian, Nina Uraltseva.

Format:

Book

Author/Creator:

Petrosyan, Arshak, 1975- author.

Shahgholian, Henrik, 1960- 700, author.

Uraltseva, N. N. (Nina Nikolaevna), author.

Series:

Graduate studies in mathematics ; Volume 136.

Graduate Studies in Mathematics ; Volume 136

Language:

English

Subjects (All):

Boundary value problems.

Physical Description:

1 online resource (225 p.)

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2012.

Language Note:

English

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 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.

Contents:

""Cover""; ""Title page""; ""Contents""; ""Preface""; ""Introduction""; ""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""; ""Bibliography""; ""Notation""; ""Index""; ""Back Cover""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-8218-8991-5