Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem.
Danielli, Donatella.
Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem. - 1st ed. - 1 online resource (90 pages) - Memoirs of the American Mathematical Society ; v.249 . - Memoirs of the American Mathematical Society .
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Regularity of geodesic foliations -- 2.1. Transport rays -- 2.2. Whitney's extension theorem for ^ -- 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 ^-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.
9781470441296
Elasticity-Mathematical models.
Boundary value problems.
Mathematical physics.
Electronic books.
QA931 .D365 2017
531.382
Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem. - 1st ed. - 1 online resource (90 pages) - Memoirs of the American Mathematical Society ; v.249 . - Memoirs of the American Mathematical Society .
Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Regularity of geodesic foliations -- 2.1. Transport rays -- 2.2. Whitney's extension theorem for ^ -- 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 ^-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.
9781470441296
Elasticity-Mathematical models.
Boundary value problems.
Mathematical physics.
Electronic books.
QA931 .D365 2017
531.382