
Journal of Convex Analysis 31 (2024), No. 2, 477496 Copyright Heldermann Verlag 2024 Stochastic Homogenization of a Class of Quasiconvex and Possibly Degenerate Viscous HJ Equations in 1D Andrea Davini Dipartimento di Matematica, Università La Sapienza, Roma, Italy davini@mat.uniroma1.it We prove homogenization for possibly degenerate viscous HamiltonJacobi equations with a Hamiltonian of the form G(p)+V(x, ω), where G is a quasiconvex, locally Lipschitz function with superlinear growth, the potential V(x, ω) is bounded and Lipschitz continuous, and the diffusion coefficient a(x, ω) is allowed to vanish on some regions or even on the whole of R. The class of random media we consider is defined by an explicit scaled hill condition on the pair (a,V) which is fulfilled as long as the environment is not "rigid". Keywords: Viscous HamiltonJacobi equation, stochastic homogenization, stationary ergodic random environment, sublinear corrector, viscosity solution, scaled hill and valley condition. MSC: 35B27, 35F21, 60G10. [ Fulltextpdf (188 KB)] for subscribers only. 