A fundamental solution for a subelliptic operator in Finsler geometry
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909071501688832 |
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| author | Dragoni, Federica Garofalo, Nicola Giovannardi, Gianmarco Salani, Paolo |
| author_facet | Dragoni, Federica Garofalo, Nicola Giovannardi, Gianmarco Salani, Paolo |
| contents | We introduce a class of nonlinear partial differential equations in a product space which are at the interface of Finsler and sub-Riemannian geometry. To such equations we associate a non-isotropic Minkowski gauge $Θ$ for which we introduce a suitable notion of Legendre transform $Θ^0$. We compute the action of the relevant nonlinear PDEs on ``radial" functions, i.e., functions of $Θ^0$, and by exploiting it we are able to compute explicit fundamental solutions of such PDEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06736 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A fundamental solution for a subelliptic operator in Finsler geometry Dragoni, Federica Garofalo, Nicola Giovannardi, Gianmarco Salani, Paolo Analysis of PDEs Differential Geometry 35H20, 35A08, 35R03, 35J62, 58J60 We introduce a class of nonlinear partial differential equations in a product space which are at the interface of Finsler and sub-Riemannian geometry. To such equations we associate a non-isotropic Minkowski gauge $Θ$ for which we introduce a suitable notion of Legendre transform $Θ^0$. We compute the action of the relevant nonlinear PDEs on ``radial" functions, i.e., functions of $Θ^0$, and by exploiting it we are able to compute explicit fundamental solutions of such PDEs. |
| title | A fundamental solution for a subelliptic operator in Finsler geometry |
| topic | Analysis of PDEs Differential Geometry 35H20, 35A08, 35R03, 35J62, 58J60 |
| url | https://arxiv.org/abs/2401.06736 |