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arXiv · 2207.04864

The fundamental gap of a kind of two dimensional sub-elliptic operator

Hongli Sun·Donghui Yang·Xu Zhang
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Abstract

This paper is concerned at the minimization fundamental gap problem for a class of two-dimensional degenerate sub-elliptic operators. We establish existence results for weak solutions, Sobolev embedding theorem and spectral theory of sub-elliptic operators. We provide the existence and characterization theorems for extremizing potentials $V(x)$ when $V(x)$ is subject to $L^\infty$ norm constraint.

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Hongli Sun, Donghui Yang, Xu Zhang. 2022-07-11. The fundamental gap of a kind of two dimensional sub-elliptic operator. https://arxiv.org/abs/2207.04864

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