Higher regularity for the fractional thin obstacle problem
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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article (Journal) |
| Language: | English |
| Published: |
2019
|
| In: |
New York journal of mathematics
Year: 2019, Volume: 25, Pages: 745-838 |
| ISSN: | 1076-9803 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://www.emis.de/journals/NYJM/j/2019/25-35p.pdf
|
| Author Notes: | Herbert Koch, Angkana Rüland and Wenhui Shi |
| Summary: | 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. |
|---|---|
| Item Description: | Gesehen am 27.05.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1076-9803 |