Optimal regularity and the free boundary in the parabolic Signorini problem

Donatella Danielli, Nicola Garofalo, Arshak Petrosyan, Tung To

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1-116
Number of pages116
JournalMemoirs of the American Mathematical Society
Issue number1181
StatePublished - Sep 2017
Externally publishedYes


  • 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

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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