@article{2a84d6bfa8114916b27e0e8e3b642953,

title = "Optimal regularity and the free boundary in the parabolic Signorini problem",

abstract = "We 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.",

keywords = "Almgren's frequency formula, Caffarelli's monotonicity formula, Evolutionary variational inequality, Free boundary problem, Monneau's monotonicity formula, Optimal regularity, Parabolic Signorini problem, Regularity of free boundary, Singular set, Weiss's monotonicity formula",

author = "Donatella Danielli and Nicola Garofalo and Arshak Petrosyan and Tung To",

note = "Funding Information: Received by the editor November 23, 2014 and, in revised form, May 12, 2015. Article electronically published on August 8, 2017. DOI: http://dx.doi.org/10.1090/memo/1181 2010 Mathematics Subject Classification. Primary 35R35, 35K85. Key words and phrases. Free boundary problem, parabolic Signorini problem, evolutionary variational inequality, Almgren{\textquoteright}s frequency formula, Caffarelli{\textquoteright}s monotonicity formula, Weiss{\textquoteright}s monotonicity formula, Monneau{\textquoteright}s monotonicity formula, optimal regularity, regularity of free boundary, singular set. Donatella Danielli is affiliated with the Department of Mathematics, Purdue University, West Lafayette, Indiana 47907. E-mail: danielli@math.purdue.edu. The first author was supported in part by NSF grant DMS-1101246. Nicola Garofalo is affiliated with the Dipartimento d{\textquoteright}Ingegneria Civile e Ambientale (DICEA), Universit{\`a} di Padova, via Trieste 63, 35131 Padova, Italy. E-mail: nicola.garofalo@unipd.it. The second author was supported in part by NSF grant DMS-1001317. Arshak Petrosyan is affiliated with the Department of Mathematics, Purdue University, West Lafayette, Indiana 47907. E-mail: arshak@math.purdue.edu. The third author was supported in part by NSF grant DMS-1101139. Tung To is affiliated with the Department of Mathematics, Purdue University, West Lafayette, Indiana 47907. E-mail: totung@gmail.com. Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.",

year = "2017",

month = sep,

doi = "10.1090/memo/1181",

language = "English (US)",

volume = "249",

pages = "1--116",

journal = "Memoirs of the American Mathematical Society",

issn = "0065-9266",

publisher = "American Mathematical Society",

number = "1181",

}