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arXiv · 2401.06736

A fundamental solution for a subelliptic operator in Finsler geometry

Federica Dragoni·Nicola Garofalo·Gianmarco Giovannardi·Paolo Salani
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Abstract

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 $\Theta$ for which we introduce a suitable notion of Legendre transform $\Theta^0$. We compute the action of the relevant nonlinear PDEs on ``radial" functions, i.e., functions of $\Theta^0$, and by exploiting it we are able to compute explicit fundamental solutions of such PDEs.

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Federica Dragoni, Nicola Garofalo, Gianmarco Giovannardi, Paolo Salani. 2024-01-12. A fundamental solution for a subelliptic operator in Finsler geometry. https://arxiv.org/abs/2401.06736

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