A fundamental solution for a subelliptic operator in Finsler geometry

Fuente: arXiv
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Main Authors: Dragoni, Federica, Garofalo, Nicola, Giovannardi, Gianmarco, Salani, Paolo
Format: Preprint
Published: 2024
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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