An epiperimetric inequality approach to the parabolic signorini problem

Wenhui Shi

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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
Issue number3
Publication statusPublished - Mar 2020


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

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