Abstract
Given g an \(\alpha \)-Hölder continuous function defined on the boundary of a bounded domain \(\Omega \) and given \(\psi \) a continuous obstacle defined in \(\overline{\Omega }\), in this article, we find u an \(\alpha \)-Hölder extension of g in \(\Omega \) with \(u\ge \psi \). This function u minimizes the \(\alpha \)-Hölder semi-norm of all possible extensions with these properties and it is a viscosity solution of the associated obstacle problem for the infinity fractional Laplace operator.
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Notes
Recall that \((C^{0,\alpha }({\Omega }), ||.||_\infty + [.]_{\alpha })\) is a Banach Space.
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Acknowledgements
The first author was supported by MINECO-FEDER grant MTM2015-68210-P, Junta de Andalucía FQM-116 and Ministerio de Educación, Cultura y Deporte (Spain) FPU Grant FPU12/02395. The second author was partially supported by IEMath-Granada, CONICET and Secyt-UNC.
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Moreno Mérida, L., Vidal, R.E. The obstacle problem for the infinity fractional laplacian. Rend. Circ. Mat. Palermo, II. Ser 67, 7–15 (2018). https://doi.org/10.1007/s12215-016-0286-2
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DOI: https://doi.org/10.1007/s12215-016-0286-2