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Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2017Copyright date: ©2017Edition: 1st edDescription: 1 online resource (90 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470441296
Subject(s): Genre/Form: Additional physical formats: Print version:: Optimal Regularity and the Free Boundary in the Parabolic Signorini ProblemDDC classification:
  • 531.382
LOC classification:
  • QA931 .D365 2017
Online resources:
Contents:
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Regularity of geodesic foliations -- 2.1. Transport rays -- 2.2. Whitney's extension theorem for ^{1,1} -- 2.3. Riemann normal coordinates -- 2.4. Proof of the regularity theorem -- Chapter 3. Conditioning a measure with respect to a geodesic foliation -- 3.1. Geodesics emanating from a ^{1,1}-hypersurface -- 3.2. Decomposition into ray clusters -- 3.3. Needles and Ricci curvature -- Chapter 4. The Monge-Kantorovich problem -- Chapter 5. Some applications -- 5.1. The inequalities of Buser, Ledoux and E. Milman -- 5.2. A Poincaré inequality for geodesically-convex domains -- 5.3. The isoperimetric inequality and its relatives -- Chapter 6. Further research -- Appendix: The Feldman-McCann proof of Lemma 2.4.1 -- Bibliography -- Back Cover.
Summary: The authors give a comprehensive treatment of the parabolic Signorini problem based on a generalization of Almgren's monotonicity of the frequency. This includes the proof of the optimal regularity of solutions, classification of free boundary points, the regularity of the regular set and the structure of the singular set.
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Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Regularity of geodesic foliations -- 2.1. Transport rays -- 2.2. Whitney's extension theorem for ^{1,1} -- 2.3. Riemann normal coordinates -- 2.4. Proof of the regularity theorem -- Chapter 3. Conditioning a measure with respect to a geodesic foliation -- 3.1. Geodesics emanating from a ^{1,1}-hypersurface -- 3.2. Decomposition into ray clusters -- 3.3. Needles and Ricci curvature -- Chapter 4. The Monge-Kantorovich problem -- Chapter 5. Some applications -- 5.1. The inequalities of Buser, Ledoux and E. Milman -- 5.2. A Poincaré inequality for geodesically-convex domains -- 5.3. The isoperimetric inequality and its relatives -- Chapter 6. Further research -- Appendix: The Feldman-McCann proof of Lemma 2.4.1 -- Bibliography -- Back Cover.

The authors give a comprehensive treatment of the parabolic Signorini problem based on a generalization of Almgren's monotonicity of the frequency. This includes the proof of the optimal regularity of solutions, classification of free boundary points, the regularity of the regular set and the structure of the singular set.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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