Title: A geometric approach to free boundary problems
First published: 2005
Description: "Free boundary (or moving boundary or phase transition) problems surface in many areas of analysis, geometry, and applied mathematics. A typical example is the evolving interphase between a solid and liquid phase: if we know the initial configuration well enough, we should be able to reconstruct its evolution, in particular, the evolution of the interphase. In this book we present a series of ideas, methods, and techniques for treating the most basic issues of such a problem. In particular, we describe the very fundamental tools of geometry and real analysis that make this possible: properties of harmonic and caloric measures in Lipschitz domains, a relation between parallel surfaces and elliptic equations, monotonicity formulas and rigidity, etc. We hope that the tools and ideas presented here will serve as a basis for the study of more complex phenomena and problems."--BOOK JACKET
Subjects: Lipschitz spaces, Boundary value problems
LC classification: QA379 .C34 2005