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In this paper we find the optimal regularity for viscosity solutions of the pseudo infinity laplacian. We prove that the solutions are locally Lipschitz and show an example that proves that this result is optimal. We also show existence and uniqueness for the Dirichlet problem.
@article{COCV_2007__13_2_294_0,
author = {Rossi, Julio D. and Saez, Mariel},
title = {Optimal regularity for the pseudo infinity laplacian},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {294--304},
publisher = {EDP-Sciences},
volume = {13},
number = {2},
year = {2007},
doi = {10.1051/cocv:2007018},
mrnumber = {2306637},
zbl = {1129.35087},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007018/}
}
TY - JOUR AU - Rossi, Julio D. AU - Saez, Mariel TI - Optimal regularity for the pseudo infinity laplacian JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2007 SP - 294 EP - 304 VL - 13 IS - 2 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007018/ DO - 10.1051/cocv:2007018 LA - en ID - COCV_2007__13_2_294_0 ER -
%0 Journal Article %A Rossi, Julio D. %A Saez, Mariel %T Optimal regularity for the pseudo infinity laplacian %J ESAIM: Control, Optimisation and Calculus of Variations %D 2007 %P 294-304 %V 13 %N 2 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007018/ %R 10.1051/cocv:2007018 %G en %F COCV_2007__13_2_294_0
Rossi, Julio D.; Saez, Mariel. Optimal regularity for the pseudo infinity laplacian. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 2, pp. 294-304. doi: 10.1051/cocv:2007018
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