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Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem
 
Donatella Danielli :  Purdue University, West Lafayette, Indiana, USA
Nicola Garofalo :  and Università di Padova, Padova, Italy
Arshak Petrosyan :  Purdue University, West Lafayette, Indiana, USA
Tung To :  Purdue University, West Lafayette, Indiana, USA
Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem
eBook ISBN:  978-1-4704-4129-6
Product Code:  MEMO/249/1181.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $45.00
Add to cart
Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem
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Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem
Donatella Danielli :  Purdue University, West Lafayette, Indiana, USA
Nicola Garofalo :  and Università di Padova, Padova, Italy
Arshak Petrosyan :  Purdue University, West Lafayette, Indiana, USA
Tung To :  Purdue University, West Lafayette, Indiana, USA
eBook ISBN:  978-1-4704-4129-6
Product Code:  MEMO/249/1181.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $45.00
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 249; 2017; 103 pp
    MSC: Primary 35

    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.
  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Notation and preliminaries
    • 3. Known existence and regularity results
    • 4. Classes of solutions
    • 5. Estimates in Gaussian spaces
    • 6. The generalized frequency function
    • 7. Existence and homogeneity of blowups
    • 8. Homogeneous global solutions
    • 9. Optimal regularity of solutions
    • 10. Classification of free boundary points
    • 11. Free boundary: Regular set
    • 12. Free boundary: Singular set
    • 13. Weiss and Monneau type monotonicity formulas
    • 14. Structure of the singular set
    • A. Estimates in Gaussian spaces: Proofs
    • B. Parabolic Whitney’s extension theorem
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 249; 2017; 103 pp
MSC: Primary 35

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.
  • Chapters
  • 1. Introduction
  • 2. Notation and preliminaries
  • 3. Known existence and regularity results
  • 4. Classes of solutions
  • 5. Estimates in Gaussian spaces
  • 6. The generalized frequency function
  • 7. Existence and homogeneity of blowups
  • 8. Homogeneous global solutions
  • 9. Optimal regularity of solutions
  • 10. Classification of free boundary points
  • 11. Free boundary: Regular set
  • 12. Free boundary: Singular set
  • 13. Weiss and Monneau type monotonicity formulas
  • 14. Structure of the singular set
  • A. Estimates in Gaussian spaces: Proofs
  • B. Parabolic Whitney’s extension theorem
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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