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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.
@article{COCV_2012__18_3_799_0,
author = {Chambolle, Antonin and Lindgren, Erik and Monneau, R\'egis},
title = {A {H\"older} infinity laplacian},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {799--835},
publisher = {EDP-Sciences},
volume = {18},
number = {3},
year = {2012},
doi = {10.1051/cocv/2011182},
mrnumber = {3041665},
zbl = {1255.35078},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011182/}
}
TY - JOUR AU - Chambolle, Antonin AU - Lindgren, Erik AU - Monneau, Régis TI - A Hölder infinity laplacian JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 799 EP - 835 VL - 18 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011182/ DO - 10.1051/cocv/2011182 LA - en ID - COCV_2012__18_3_799_0 ER -
%0 Journal Article %A Chambolle, Antonin %A Lindgren, Erik %A Monneau, Régis %T A Hölder infinity laplacian %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 799-835 %V 18 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011182/ %R 10.1051/cocv/2011182 %G en %F COCV_2012__18_3_799_0
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
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