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 in . 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.
Mots clés : 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://archive.numdam.org/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://archive.numdam.org/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://archive.numdam.org/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. http://archive.numdam.org/articles/10.1016/j.anihpc.2014.09.010/
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