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Full Description
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.
Contents
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.
