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

Abstract

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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.

How to cite

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Chambolle, 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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  11. H. Lebesgue, Sur le problème de Dirichlet. Rend. Circ. Mat. Palermo24 (1907) 371–402.  
  12. G. Lu and P. Wang, Inhomogeneous infinity Laplace equation. Adv. Math.217 (2008) 1838–1868.  Zbl1152.35042
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