Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem

Donatella Danielli, Purdue University, West Lafayette, Indiana.Nicola Garofalo, Universita di Padova, Italy.Arshak Petrosyan, Purdue University, West Lafayette, Indiana.Tung To, Purdue University, West Lafayette, Indiana.

• IntroductionNotation and preliminariesKnown existence and regularity resultsClasses of solutionsEstimates in Gaussian spacesThe generalized frequency functionExistence and homogeneity of blowupsHomogeneous global solutionsOptimal regularity of solutionsClassification of free boundary pointsFree boundary: Regular setFree boundary: Singular setWeiss and Monneau type monotonicity formulasStructure of the singular set}Appendix A. Estimates in Gaussian spaces: ProofsAppendix B. Parabolic Whitney's extension theoremBibliography.