A partial homogenization result for nonconvex viscous Hamilton-Jacobi equations
We provide a general result concerning the homogenization of nonconvex viscous Hamilton-Jacobi equations in the stationary, ergodic setting. In particular, we show that homogenization occurs for a non-empty set of points within every level set of the effective Hamiltonian, and for every point in the...
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| Format: | Journal article |
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2014
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| _version_ | 1826297141806497792 |
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| author | Fehrman, B |
| author_facet | Fehrman, B |
| author_sort | Fehrman, B |
| collection | OXFORD |
| description | We provide a general result concerning the homogenization of nonconvex viscous Hamilton-Jacobi equations in the stationary, ergodic setting. In particular, we show that homogenization occurs for a non-empty set of points within every level set of the effective Hamiltonian, and for every point in the minimal level set of the effective Hamiltonian. In addition, these methods provide a new proof of homogenization, in full, for convex equations and, for a class of level-set convex equations. Finally, we prove that the question of homogenization for first order equations reduces to the case that the nonconvexity of the Hamiltonian is localized in the gradient variable |
| first_indexed | 2024-03-07T04:27:03Z |
| format | Journal article |
| id | oxford-uuid:cd0091e5-0f0d-4ef3-ace3-3761a6d1ed76 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:27:03Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | oxford-uuid:cd0091e5-0f0d-4ef3-ace3-3761a6d1ed762022-03-27T07:25:46ZA partial homogenization result for nonconvex viscous Hamilton-Jacobi equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:cd0091e5-0f0d-4ef3-ace3-3761a6d1ed76Symplectic Elements at Oxford2014Fehrman, BWe provide a general result concerning the homogenization of nonconvex viscous Hamilton-Jacobi equations in the stationary, ergodic setting. In particular, we show that homogenization occurs for a non-empty set of points within every level set of the effective Hamiltonian, and for every point in the minimal level set of the effective Hamiltonian. In addition, these methods provide a new proof of homogenization, in full, for convex equations and, for a class of level-set convex equations. Finally, we prove that the question of homogenization for first order equations reduces to the case that the nonconvexity of the Hamiltonian is localized in the gradient variable |
| spellingShingle | Fehrman, B A partial homogenization result for nonconvex viscous Hamilton-Jacobi equations |
| title | A partial homogenization result for nonconvex viscous Hamilton-Jacobi
equations |
| title_full | A partial homogenization result for nonconvex viscous Hamilton-Jacobi
equations |
| title_fullStr | A partial homogenization result for nonconvex viscous Hamilton-Jacobi
equations |
| title_full_unstemmed | A partial homogenization result for nonconvex viscous Hamilton-Jacobi
equations |
| title_short | A partial homogenization result for nonconvex viscous Hamilton-Jacobi
equations |
| title_sort | partial homogenization result for nonconvex viscous hamilton jacobi equations |
| work_keys_str_mv | AT fehrmanb apartialhomogenizationresultfornonconvexviscoushamiltonjacobiequations AT fehrmanb partialhomogenizationresultfornonconvexviscoushamiltonjacobiequations |