H^1+α estimates for the fully nonlinear parabolic thin obstacle problem

2022/01/22 by Hu, Xi, Tang, Lin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.03878

Abstract

We study the regularity of the viscosity solution to the fully nonlinear parabolic thin obstacle problem. In particular, we prove that the solution is local H^1+α on each side of the smooth obstacle, for some small α>0. Following the method which was first introduced for the harmonic case by Caffarelli in 1979, we extend the results of Fernández-Real (2016) who treated the fully nonlinear elliptic case. Our results also extend those of Chatzigeorgiou (2019) in two ways. First, we do not assume solutions nor operators to be symmetric. Second, our estimates are local, in the sense that do not rely on the boundary data.

Related

• Regularity for the fully nonlinear parabolic thin obstacle problem
• C^1,α estimates for the fully nonlinear Signorini problem
• Regularity theory for fully nonlinear parabolic obstacle problems
• The regular free boundary in the thin obstacle problem for degenerate parabolic equations
• Sharp regularity for a singular fully nonlinear parabolic free boundary problem