Principal eigenvalue problem for infinity Laplacian in metric spaces

DOI10.1515/ANS-2022-0028zbMATH Open1501.35273arXiv2109.08897OpenAlexW4312745679MaRDI QIDQ2093688

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Publication date: 27 October 2022

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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.

Full work available at URL: https://arxiv.org/abs/2109.08897

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