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A Geometric Approach to Free Boundary Problems

About this Title

Luis Caffarelli, University of Texas, Austin, TX and Sandro Salsa, Politecnico di Milano, Milan, Italy

Publication: Graduate Studies in Mathematics
Publication Year: 2005; Volume 68
ISBNs: 978-0-8218-3784-9 (print); 978-1-4704-2109-0 (online)
DOI: https://doi.org/10.1090/gsm/068
MathSciNet review: MR2145284
MSC: Primary 35R35; Secondary 35-01, 35J25, 35K20

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Table of Contents

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Front/Back Matter

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Part 1. Elliptic problems

• Chapter 1. An introductory problem
• Chapter 2. Viscosity solutions and their asymptotic developments
• Chapter 3. The regularity of the free boundary
• Chapter 4. Lipschitz free boundaries are $C^{1,\gamma }$
• Chapter 5. Flat free boundaries are Lipschitz
• Chapter 6. Existence theory

Part 2. Evolution problems

• Chapter 7. Parabolic free boundary problems
• Chapter 8. Lipschitz free boundaries: Weak results
• Chapter 9. Lipschitz free boundaries: Strong results
• Chapter 10. Flat free boundaries are smooth

Part 3. Complementary chapters: Main tools

• Chapter 11. Boundary behavior of harmonic functions
• Chapter 12. Monotonicity formulas and applications
• Chapter 13. Boundary behavior of caloric functions