An epiperimetric inequality approach to the parabolic signorini problem

Wenhui Shi

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7 Citations (Scopus)

Abstract

In this note, we use an epiperimetric inequality approach to study the regularity of the free boundary for the parabolic Signorini problem. We show that if the \vanishing order" of a solution at a free boundary point is close to 3=2 or an even integer, then the solution is asymptotically homogeneous. Furthermore, one can derive a convergence rate estimate towards the asymptotic homogeneous solution. As a consequence, we obtain the regularity of the regular free boundary as well as the frequency gap.

Original languageEnglish
Pages (from-to)1813-1846
Number of pages34
JournalDiscrete and Continuous Dynamical Systems Series A
Volume40
Issue number3
DOIs
Publication statusPublished - Mar 2020

Keywords

  • Epiperimetric inequality
  • Free boundary regularity
  • Parabolic Signorini problem
  • Singular set

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