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<p>We prove homogenization for degenerate viscous Hamilton–Jacobi equations in dimension one in stationary ergodic environments with a quasiconvex and superlinear Hamiltonian of fairly general type. We furthermore show that the effective Hamiltonian is quasiconvex. This latter result is new even in the periodic setting, despite homogenization being known for quite some time.</p>

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Stochastic homogenization of quasiconvex degenerate viscous HJ equations in 1d

  • 期刊论文

  • 发表日期：

    2025年1月6日

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  • Andrea Davini

摘要

We prove homogenization for degenerate viscous Hamilton–Jacobi equations in dimension one in stationary ergodic environments with a quasiconvex and superlinear Hamiltonian of fairly general type. We furthermore show that the effective Hamiltonian is quasiconvex. This latter result is new even in the periodic setting, despite homogenization being known for quite some time.