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A Hölder infinity Laplacian

Published online by Cambridge University Press:  17 August 2011

Antonin Chambolle ,
Erik Lindgren  and
Régis Monneau
Antonin Chambolle
Affiliation:
CMAP, École Polytechnique, 91128 Palaiseau Cedex, France. antonin.chambolle@cmap.polytechnique.fr
Erik Lindgren
Affiliation:
Dept. of Mathematical Sciences, NTNU, 7491 Trondheim, Norway; erik.lindgren@math.ntnu.no
Régis Monneau
Affiliation:
Université Paris-Est, Cermics, École des Ponts ParisTech, 6-8, avenue Blaise-Pascal, 77455 Marne-la-Vallée Cedex 2, France; monneau@cermics.enpc.fr
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Abstract

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

Keywords

Lipschitz extensionsHölder extensionsinfinity Laplaciannon-local and non-linear equationsviscosity solutions
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 3 , July 2012 , pp. 799 - 835
Copyright
© EDP Sciences, SMAI, 2011

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