Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem

ISBN-13: 9781470425470 / Angielski

Donatella Danielli;Nicola Garofalo;Arshak Petrosyan

Opis

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.

Spis treści

• 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}
• Appendix A. Estimates in Gaussian spaces: Proofs
• Appendix B. Parabolic Whitney's extension theorem
• Bibliography.