Calculus of Variations and Geometric Measure Theory

F. Dragoni - N. Garofalo - G. Giovannardi - P. Salani

A fundamental solution for a subelliptic operator in Finsler geometry

created by dragoni on 17 Jan 2024

[BibTeX]

preprint

Inserted: 17 jan 2024

Year: 2024

ArXiv: 2401.06736 PDF

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.