| Issue |
ESAIM: COCV
Volume 18, Number 3, July-September 2012
|
|
|---|---|---|
| Page(s) | 799 - 835 | |
| DOI | https://doi.org/10.1051/cocv/2011182 | |
| Published online | 17 August 2011 | |
A Hölder infinity Laplacian
1
CMAP, École Polytechnique, 91128
Palaiseau Cedex,
France
antonin.chambolle@cmap.polytechnique.fr
2
Dept. of Mathematical Sciences, NTNU, 7491
Trondheim,
Norway
erik.lindgren@math.ntnu.no
3
Université Paris-Est, Cermics, École des Ponts
ParisTech, 6-8, avenue
Blaise-Pascal, 77455
Marne-la-Vallée Cedex 2,
France
monneau@cermics.enpc.fr
Received:
7
April
2011
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.
Mathematics Subject Classification: 35D40 / 35J60 / 35J65
Key words: Lipschitz extensions / Hölder extensions / infinity Laplacian / non-local and non-linear equations / viscosity solutions
© EDP Sciences, SMAI, 2011
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