Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem

We 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 th...

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Main Authors: Danielli, Donatella, Garofalo, Nicola, Petrosyan, Arshak, To, Tung
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2017
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Boundary value problems
Elasticity
Elasticity > Mathematical models
Mathematical physics
singular set
Almgren’s frequency formula
Caffarelli’s monotonicity formula
optimal regularity
evolutionary variational inequality
Free boundary problem
regularity of free boundary
Weiss’s monotonicity formula
parabolic Signorini problem
Monneau’s monotonicity formula
ISBN:9781470425470, 1470425475
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Abstract We 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.
AbstractList We 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.
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.
Author Danielli, Donatella
Garofalo, Nicola
Petrosyan, Arshak
To, Tung
Author_xml – sequence: 1
  givenname: Donatella
  surname: Danielli
  fullname: Danielli, Donatella
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  organization: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
– sequence: 2
  givenname: Nicola
  surname: Garofalo
  fullname: Garofalo, Nicola
  email: nicola.garofalo@unipd.it
  organization: Dipartimento d’Ingegneria Civile e Ambientale (DICEA), Università di Padova, via Trieste 63, 35131 Padova, Italy
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  givenname: Arshak
  surname: Petrosyan
  fullname: Petrosyan, Arshak
  email: arshak@math.purdue.edu
  organization: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
– sequence: 4
  givenname: Tung
  surname: To
  fullname: To, Tung
  email: totung@gmail.com
  organization: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
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Keywords singular set
Almgren’s frequency formula
Caffarelli’s monotonicity formula
optimal regularity
evolutionary variational inequality
Free boundary problem
regularity of free boundary
Weiss’s monotonicity formula
parabolic Signorini problem
Monneau’s monotonicity formula
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Notes Volume 249, number 1181 (second of 8 numbers), September 2017
Bibliography: p. 101-103
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Snippet We give a comprehensive treatment of the parabolic Signorini problem based on a generalization of Almgren’s monotonicity of the frequency. This includes the...
The authors give a comprehensive treatment of the parabolic Signorini problem based on a generalization of Almgren's monotonicity of the frequency. This...
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SubjectTerms Boundary value problems
Elasticity
Elasticity -- Mathematical models
Mathematical physics
TableOfContents Introduction -- Notation and preliminaries -- Known existence and regularity results -- Classes of solutions -- Estimates in Gaussian spaces -- The generalized frequency function -- Existence and homogeneity of blowups -- Homogeneous global solutions -- Optimal regularity of solutions -- Classification of free boundary points -- Free boundary: Regular set -- Free boundary: Singular set -- Weiss and Monneau type monotonicity formulas -- Structure of the singular set -- Estimates in Gaussian spaces: Proofs -- Parabolic Whitney’s extension theorem
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
Title Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem
URI https://www.ams.org/memo/1181/
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