Regularity of almost minimizers for the parabolic thin obstacle problem

Abstract

In this paper, we study almost minimizers for the parabolic thin obstacle (or Signorini) problem with zero obstacle. We establish their Hσ,σ/2-regularity for every 0<σ<1, as well as Hβ,β/2-regularity of their spatial gradients on the either side of the thin space for some 0<β<1. A similar result is also obtained for almost minimizers for the Signorini problem with variable Hölder coefficients.