Stochastic homogenization of nonconvex viscous Hamilton-Jacobi equations in one space dimension

• Published in: Communications in partial differential equations Vol. 49; no. 7-8; pp. 698 - 734
• Main Authors: Davini, Andrea, Kosygina, Elena, Yilmaz, Atilla
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.08.2024; Taylor & Francis Ltd
• Subjects: Continuity (mathematics); Hamilton-Jacobi equation; Hamiltonian functions; Homogenization; scaled hill and valley condition; stationary ergodic random environment; stochastic homogenization; sublinear corrector; viscosity solution; Viscous Hamilton-Jacobi equation
• ISSN: 0360-5302; 1532-4133
• DOI: 10.1080/03605302.2024.2390836

We prove homogenization for viscous Hamilton-Jacobi equations with a Hamiltonian of the form G ( p ) + V ( x , ω ) for a wide class of stationary ergodic random media in one space dimension. The momentum part G(p) of the Hamiltonian is a general (nonconvex) continuous function with superlinear growth at infinity, and the potential V ( x , ω ) is bounded and Lipschitz continuous. The class of random media we consider is defined by an explicit hill and valley condition on the diffusivity-potential pair which is fulfilled as long as the environment is not "rigid".