Principal eigenvalue problem for infinity Laplacian in metric spaces
This article is concerned with the Dirichlet eigenvalue problem associated with the ∞\infty -Laplacian in metric spaces. We establish a direct partial differential equation approach to find the principal eigenvalue and eigenfunctions in a proper geodesic space without assuming any measure structure....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-10-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2022-0028 |
| Summary: | This article is concerned with the Dirichlet eigenvalue problem associated with the ∞\infty -Laplacian in metric spaces. We establish a direct partial differential equation 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 pp-Laplacian in the Euclidean space. |
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| ISSN: | 2169-0375 |