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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