Description

Book Synopsis
Describes the properties of harmonic and caloric measures in Lipschitz domains, a relation between parallel surfaces and elliptic equations, monotonicity formulas and rigidity. This book is suitable for graduate students and researchers interested in partial differential equations.

Table of Contents
Elliptic problems: An introductory problem Viscosity solutions and their asymptotic developments The regularity of the free boundary Lipschitz free boundaries are $C^{1,\gamma}$ Flat free boundaries are Lipschitz Existence theory Evolution problems: Parabolic free boundary problems Lipschitz free boundaries: Weak results Lipschitz free boundaries: Strong results Flat free boundaries are smooth Complementary chapters: Main tools: Boundary behavior of harmonic functions Monotonicity formulas and applications Boundary behavior of caloric functions Bibliography Index.

A Geometric Approach to Free Boundary Problems

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    A Hardback by Luis Caffarelli, Sandro Salsa

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      Publisher: MP-AMM American Mathematical
      Publication Date: Publication Date: 6/30/2005 12:00:00 AM
      ISBN13: 9780821837849, 978-0821837849
      ISBN10: 0821837842

      Description

      Book Synopsis
      Describes the properties of harmonic and caloric measures in Lipschitz domains, a relation between parallel surfaces and elliptic equations, monotonicity formulas and rigidity. This book is suitable for graduate students and researchers interested in partial differential equations.

      Table of Contents
      Elliptic problems: An introductory problem Viscosity solutions and their asymptotic developments The regularity of the free boundary Lipschitz free boundaries are $C^{1,\gamma}$ Flat free boundaries are Lipschitz Existence theory Evolution problems: Parabolic free boundary problems Lipschitz free boundaries: Weak results Lipschitz free boundaries: Strong results Flat free boundaries are smooth Complementary chapters: Main tools: Boundary behavior of harmonic functions Monotonicity formulas and applications Boundary behavior of caloric functions Bibliography Index.

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