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Optimal regularity and the free boundary in the parabolic Signorini problem / Donatella Danielli...[et al.].

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 249, no 1181.Publication details: Providence : American Mathematical Society, 2017.Description: v, 103 pages ; 26 cmISBN:
  • 9781470425470 (alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
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 -- Appendices.
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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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 510 Am512 (Browse shelf(Opens below)) Available 138223
Total holds: 0

Includes bibliographical references.

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 --
Appendices.

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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