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Herbert Koch,
Angkana Rüland, and
Wenhui Shi
Higher regularity for the fractional thin obstacle problem
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| Published: |
September 5, 2019. |
| Keywords: |
Variable coefficient fractional Signorini problem, variable coefficient fractional thin obstacle problem, thin free boundary, Hodograph-Legendre transform. |
| Subject: |
Primary 35R35. |
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Abstract
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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| Acknowledgements
H.K. acknowledges support by the DFG through SFB 1060, Bonn.
A.R. acknowledges a Junior Research Fellowship at Christ Church, Oxford University.
W.S. is supported by the Hausdorff Center for Mathematics, Bonn.
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| Author information
Herbert Koch:
Mathematisches Institut
Universität Bonn
Endenicher Allee 60, 53115 Bonn, Germany
koch@math.uni-bonn.de
Angkana Rüland:
Max-Planck Institute for Mathematics in the Sciences
Inselstrasse 22
04105 Leipzig, Germany
rueland@mis.mpg.de
Wenhui Shi:
School of Mathematics
Monash University
9 Rainforest Walk, 3168 Clayton, Australia
wenhui.shi@monash.edu
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