# A Hölder infinity Laplacian

Antonin Chambolle; Erik Lindgren; Régis Monneau

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 3, page 799-835
- ISSN: 1292-8119

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topChambolle, Antonin, Lindgren, Erik, and Monneau, Régis. "A Hölder infinity Laplacian." ESAIM: Control, Optimisation and Calculus of Variations 18.3 (2012): 799-835. <http://eudml.org/doc/276367>.

@article{Chambolle2012,

abstract = {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. },

author = {Chambolle, Antonin, Lindgren, Erik, Monneau, Régis},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Lipschitz extensions; Hölder extensions; infinity Laplacian; non-local and non-linear equations; viscosity solutions},

language = {eng},

month = {11},

number = {3},

pages = {799-835},

publisher = {EDP Sciences},

title = {A Hölder infinity Laplacian},

url = {http://eudml.org/doc/276367},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Chambolle, Antonin

AU - Lindgren, Erik

AU - Monneau, Régis

TI - A Hölder infinity Laplacian

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2012/11//

PB - EDP Sciences

VL - 18

IS - 3

SP - 799

EP - 835

AB - 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.

LA - eng

KW - Lipschitz extensions; Hölder extensions; infinity Laplacian; non-local and non-linear equations; viscosity solutions

UR - http://eudml.org/doc/276367

ER -

## References

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