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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.17031 |
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| _version_ | 1866910912163610624 |
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| author | Davini, Andrea |
| author_facet | Davini, Andrea |
| contents | 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 $\mathbb{R}$. 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''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17031 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic homogenization of a class of quasiconvex and possibly degenerate viscous HJ equations in 1d Davini, Andrea Analysis of PDEs 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 $\mathbb{R}$. 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''. |
| title | Stochastic homogenization of a class of quasiconvex and possibly degenerate viscous HJ equations in 1d |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.17031 |