On the hyperbolicity of minimizers for 1D random Lagrangian systems

Alexandre Boritchev (1) , Konstantin Khanin (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 Department of Mathematics

We prove hyperbolicity of global minimizers for random Lagrangian systems in dimension 1. The proof considerably simplifies a related result in [2]. The conditions for hyperbolicity are almost optimal: they are essentially the same as conditions for uniqueness of a global minimizer in [3].

Mots clés: AMS classification scheme numbers: Primary 35Q53; Secondary 35R60; 35Q35; 37H10; 76M35 Submitted to: Nonlinearity

Domaines: Equations aux dérivées partielles [math.AP]

Alexandre Boritchev, Konstantin Khanin. On the hyperbolicity of minimizers for 1D random Lagrangian systems. Nonlinearity, 2013, 26 (1), pp.65 - 80. ⟨10.1088/0951-7715/26/1/65⟩. ⟨hal-01092947⟩