In this article we investigate the higher regularity properties of the regular free boundary in the fractional thin obstacle problem. Relying on a Hodograph-Legendre transform, we show that for smooth or analytic obstacles the regular free boundary is smooth or analytic, respectively. This leads to the analysis of a fully nonlinear, degenerate (sub)elliptic operator which we identify as a (fully nonlinear) perturbation of the fractional Baouendi-Grushin Laplacian. Using its intrinsic geometry and adapted function spaces, we invoke the analytic implicit function theorem to deduce analyticity of the regular free boundary.
|Number of pages||94|
|Journal||New York Journal of Mathematics|
|Publication status||Published - 1 Jan 2019|
- Hodograph-legendre transform
- Thin free boundary
- Variable coefficient fractional signorini problem
- Variable coefficient fractional thin obstacle problem