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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.11124 |
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| _version_ | 1866914950826426368 |
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| author | Ciomaga, Adina Le, Tri Minh Ley, Olivier Topp, Erwin |
| author_facet | Ciomaga, Adina Le, Tri Minh Ley, Olivier Topp, Erwin |
| contents | We obtain the comparison principle for discontinuous viscosity sub- and supersolutions of nonlocal Hamilton-Jacobi equations, with superlinear and coercive gradient terms. The nonlocal terms are integro-differential operators in Lévy form, with general measures: $x$-dependent, possibly degenerate and without any restriction on the order. The measures must satisfy a combined Wasserstein/Total Variation-continuity assumption, which is one of the weakest conditions used in the context of viscosity approach for this type of integro-differential PDEs. The proof relies on a regularizing effect due to the gradient growth. We present several examples of applications to PDEs with different types of nonlocal operators (measures with density, operators of variable order, Lévy-Itô operators). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11124 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Comparison principle for general nonlocal Hamilton-Jacobi equations with superlinear gradient Ciomaga, Adina Le, Tri Minh Ley, Olivier Topp, Erwin Analysis of PDEs We obtain the comparison principle for discontinuous viscosity sub- and supersolutions of nonlocal Hamilton-Jacobi equations, with superlinear and coercive gradient terms. The nonlocal terms are integro-differential operators in Lévy form, with general measures: $x$-dependent, possibly degenerate and without any restriction on the order. The measures must satisfy a combined Wasserstein/Total Variation-continuity assumption, which is one of the weakest conditions used in the context of viscosity approach for this type of integro-differential PDEs. The proof relies on a regularizing effect due to the gradient growth. We present several examples of applications to PDEs with different types of nonlocal operators (measures with density, operators of variable order, Lévy-Itô operators). |
| title | Comparison principle for general nonlocal Hamilton-Jacobi equations with superlinear gradient |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.11124 |