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arXiv · 2306.05825

Extremal properties of the first eigenvalue and the fundamental gap of a sub-elliptic operator

Hongli Sun·Weijia Wu·Donghui Yang
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Abstract

We consider the problems of extreming the first eigenvalue and the fundamental gap of a sub-elliptic operator with Dirichlet boundary condition, when the potential $V$ is subjected to a $p$-norm constraint. The existence results for weak solutions, compact embedding theorem and spectral theory for sub-elliptic equation are given. Moreover, we provide the specific characteristics of the corresponding optimal potential function.

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Hongli Sun, Weijia Wu, Donghui Yang. 2023-06-09. Extremal properties of the first eigenvalue and the fundamental gap of a sub-elliptic operator. https://arxiv.org/abs/2306.05825

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