We consider almost minimizers for the parabolic thin obstacle (or Signorini) problem with zero obstacle. We establish their $H^{\\sigma, \\sigma\/2}$-regularity for every $0<\\sigma<1$, as well as $H^{\\beta,\\beta\/2}$-regularity of their spatial gradients on the either side of the thin space for some $0<\\beta<1$. We then extend these regularity results to the variable H\u00f6lder continuous coefficient setting. We also discuss the regularity of the “regular” part of the free boundary. This is based on joint work with Arshak Petrosyan.<\/p>\n","protected":false},"excerpt":{"rendered":"
We consider almost minimizers for the parabolic thin obstacle (or Signorini) problem with zero obstacle. We establish their $H^{\\sigma, \\sigma\/2}$-regularity for…<\/p>\n