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...
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| Main Authors: | , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
21 May 2016
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| In: |
Arxiv
Year: 2016, Pages: 1-79 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1605.06662
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| Author Notes: | Herbert Koch, Angkana Rüland, and Wenhui Shi |
MARC
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| 520 | |a 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. | ||
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