Optimal regularity for the variable coefficients parabolic Signorini problem
Abstract
In this paper we discuss the optimal regularity of the variable coefficient parabolic Signorini problem with $W^{1,1}_p$ coefficients and $L^p$ inhomogeneity, where $p>n+2$ with $n$ being the space dimension. Relying on an parabolic Carleman estimate and an epiperimetric inequality, we show the optimal regularity of the solutions as well as the regularity of the regular free boundary.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Mathematical Modeling in Engineering
Numerical methods in inverse problems
Publication details
- Journal / source
- Indiana University Mathematics Journal
- Publisher
- Indiana University Mathematics Journal
- Volume
- 75
- Issue
- 3
- Pages
- 883–973
- Publication date
- 1 January 2026
- Language
- EN