Optimal regularity for the thin obstacle problem with CO,α coefficients
In this article we study solutions to the (interior) thin obstacle problem under low regularity assumptions on the coefficients, the obstacle and the underlying manifold. Combining the linearization method of Andersson \cite{An16} and the epiperimetric inequality from \cite{FS16}, \cite{GPSVG15}, we...
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) Kapitel/Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
26 Oct 2016
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| In: |
Arxiv
Year: 2016, Pages: 1-37 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1610.07961
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| Verfasserangaben: | Angkana Rüland and Wenhui Shi |
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| 246 | 3 | 3 | |a Optimal regularity for the thin obstacle problem with C O, alpha coefficients |
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| 520 | |a In this article we study solutions to the (interior) thin obstacle problem under low regularity assumptions on the coefficients, the obstacle and the underlying manifold. Combining the linearization method of Andersson \cite{An16} and the epiperimetric inequality from \cite{FS16}, \cite{GPSVG15}, we prove the optimal $C^{1,\min\{\alpha,1/2\}}$ regularity of solutions in the presence of $C^{0,\alpha}$ coefficients $a^{ij}$ and $C^{1,\alpha}$ obstacles $\phi$. Moreover we investigate the regularity of the regular free boundary and show that it has the structure of a $C^{1,\gamma}$ manifold for some $\gamma \in (0,1)$. | ||
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