Free or moving boundary problems are common in may areas of mathematics and science, including shape optimization, phase transitions, fluid dynamics, probability and statistics. This text covers such topics in free boundary problems as elliptic problems (such as viscosity solutions and they asymptotic developments), evolution problems (such as Lipschitz free boundaries), main tools such as the boundary behavior of harmonic functions and caloric functions and monotonicity formulas and their applications. Annotation �2005 Book News, Inc., Portland, OR (booknews.com)

Review

The book will be a great resource, especially for scientists with an application in mind who want to find out what a free boundary problem-based approach can offer them. ... The book is written by two of the most renowned specialists in the study of free boundary problems, with deep contributions in this field. ... For anyone who later will do research on free boundary problems, this is probably the best introduction ever written. But the potential audience of this volume is much wider; his approach is just right for a book at the introductory level. The result is not only a comprehensive overview of the area itself, but also a very informative and inspiring monograph. Overall, this is a fine text for a graduate or postgraduate course in free boundary problems and a valuable reference that should be on the shelves of researchers and those teaching applied partial differential equations. --Vicentiu Radulescu, MAA Reviews

In this very interesting and well-written book, the authors present many techniques and ideas to investigate free boundary problems (hereafter, denoted FBP) of both elliptic and parabolic type. --Mathematical Reviews

The tools and ideas presented in this book will serve as a basis for the study of more complex phenomena and problems. The book is well-written and the style is clear. It is suitable for graduate students and researchers interested in partial differential equations. --Zentralblatt MATH

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