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arXiv · 2109.08897

Principal eigenvalue problem for infinity Laplacian in metric spaces

Qing Liu·Ayato Mitsuishi
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Abstract

This paper is concerned with the Dirichlet eigenvalue problem associated to the $\infty$-Laplacian in metric spaces. We establish a direct PDE approach to find the principal eigenvalue and eigenfunctions in a proper geodesic space without assuming any measure structure. We provide an appropriate notion of solutions to the $\infty$-eigenvalue problem and show the existence of solutions by adapting Perron's method. Our method is different from the standard limit process via the variational eigenvalue formulation for $p$-Laplacian in the Euclidean space.

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Qing Liu, Ayato Mitsuishi. 2021-09-18. Principal eigenvalue problem for infinity Laplacian in metric spaces. https://arxiv.org/abs/2109.08897

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