A Hölder infinity laplacian
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 799-835.

In this paper we study the limit as p → ∞ of minimizers of the fractional Ws,p-norms. In particular, we prove that the limit satisfies a non-local and non-linear equation. We also prove the existence and uniqueness of solutions of the equation. Furthermore, we prove the existence of solutions in general for the corresponding inhomogeneous equation. By making strong use of the barriers in this construction, we obtain some regularity results.

DOI : 10.1051/cocv/2011182
Classification : 35D40, 35J60, 35J65
Mots-clés : Lipschitz extensions, Hölder extensions, infinity laplacian, non-local and non-linear equations, viscosity solutions 
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     title = {A {H\"older} infinity laplacian},
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Chambolle, Antonin; Lindgren, Erik; Monneau, Régis. A Hölder infinity laplacian. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 3, pp. 799-835. doi : 10.1051/cocv/2011182. http://archive.numdam.org/articles/10.1051/cocv/2011182/

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