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hölder extensions

ESAIM: Control, Optimisation and Calculus of Variations (1)

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A Hölder infinity Laplacian
Antonin Chambolle, Erik Lindgren, Régis Monneau
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 18 / Issue 3 / July 2012

Published online by Cambridge University Press:

17 August 2011, pp. 799-835

Print publication:

July 2012
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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.