Stochastic homogenization of a class of quasiconvex and possibly degenerate viscous HJ equations in 1d

2024/02/26 by Andrea Davini, Davini, Andrea
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2402.17031

openalex publication_date 2024/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove homogenization for possibly degenerate viscous Hamilton-Jacobi 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 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''.

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• Stochastic homogenization of quasiconvex degenerate viscous HJ equations in 1d
• Stochastic homogenization of nondegenerate viscous HJ equations in 1d
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