Stochastic homogenization of nondegenerate viscous HJ equations in 1d

2023/06/21 by Davini, Andrea
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2306.12145

Abstract

We prove homogenization for a nondegenerate viscous Hamilton-Jacobi equation in dimension one in stationary ergodic environments with a superlinear (nonconvex) Hamiltonian of fairly general type. The version of the paper herein posted is identical to the one submitted to the journal *** for publication on the 26th of February, 2024. One of the crucial idea for the proof corresponds to Theorem 4.2. This theorem, together with its proof, already appeared, in essential identical form, in the ArXiv e-print 2306.12145, version 1 (posted on the 21st of June 2023), see Theorem 4.5 therein.

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• Stochastic homogenization of quasiconvex degenerate viscous HJ equations in 1d
• Stochastic homogenization of nonconvex viscous Hamilton-Jacobi equations in one space dimension
• Stochastic homogenization of a class of quasiconvex viscous\n Hamilton-Jacobi equations in one space dimension
• Stochastic homogenization of a class of quasiconvex and possibly degenerate viscous HJ equations in 1d
• Homogenization of nonconvex viscous Hamilton-Jacobi equations in stationary ergodic media in one dimension