Geodesic
Existence and regularity of strict critical subsolutions in the stationary ergodic setting
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 2, pp. 243-272

Voir la notice de l'article provenant de la source Numdam

We prove that any continuous and convex stationary ergodic Hamiltonian admits critical subsolutions, which are strict outside the random Aubry set. They make up, in addition, a dense subset of all critical subsolutions with respect to a suitable metric. If the Hamiltonian is additionally assumed of Tonelli type, then there exist strict subsolutions of class C1,1 in RN. The proofs are based on the use of Lax–Oleinik semigroups and their regularizing properties in the stationary ergodic environment, as well as on a generalized notion of Aubry set.

DOI : 10.1016/j.anihpc.2014.09.010
Classification : 35D40, 35B27, 35F21, 49L25
Keywords: Stationary ergodic setting, Weak KAM Theory, Homogenization, Viscosity solutions 
@article{AIHPC_2016__33_2_243_0,
     author = {Davini, Andrea and Siconolfi, Antonio},
     title = {Existence and regularity of strict critical subsolutions in the stationary ergodic setting},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {243--272},
     publisher = {Elsevier},
     volume = {33},
     number = {2},
     year = {2016},
     doi = {10.1016/j.anihpc.2014.09.010},
     zbl = {1336.35114},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.09.010/}
}
TY  - JOUR
AU  - Davini, Andrea
AU  - Siconolfi, Antonio
TI  - Existence and regularity of strict critical subsolutions in the stationary ergodic setting
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2016
SP  - 243
EP  - 272
VL  - 33
IS  - 2
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.09.010/
DO  - 10.1016/j.anihpc.2014.09.010
LA  - en
ID  - AIHPC_2016__33_2_243_0
ER  - 
%0 Journal Article
%A Davini, Andrea
%A Siconolfi, Antonio
%T Existence and regularity of strict critical subsolutions in the stationary ergodic setting
%J Annales de l'I.H.P. Analyse non linéaire
%D 2016
%P 243-272
%V 33
%N 2
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.09.010/
%R 10.1016/j.anihpc.2014.09.010
%G en
%F AIHPC_2016__33_2_243_0
Davini, Andrea; Siconolfi, Antonio. Existence and regularity of strict critical subsolutions in the stationary ergodic setting. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 2, pp. 243-272. doi: 10.1016/j.anihpc.2014.09.010

Cité par Sources :