An Eigenvalue problem for the Infinity-Laplacian

Tilak Bhattacharya; Leonardo Marazzi

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arXiv · 1211.3074

An Eigenvalue problem for the Infinity-Laplacian

Tilak Bhattacharya·Leonardo Marazzi

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Abstract

We study an eigenvalue problem for the infinity-Laplacian on bounded domains. We prove the existence of the principal eigenvalue and a corresponding positive eigenfunction. The work also contains existence results when the parameter, in the equation, is less than the first eigenvalue. A comparison principle applicable to these problems is also proven. Some additional results are shown, in particular, that on star- shaped domains and on C^2 domains higher eigenfunctions change sign. When the domain is a ball, we prove that the first eigenfunction has one sign, radial principal eigenfunction exist and are unique up to scalar multiplication, and that there are infinitely many eigenvalues.

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Tilak Bhattacharya, Leonardo Marazzi. 2012-11-13. An Eigenvalue problem for the Infinity-Laplacian. https://arxiv.org/abs/1211.3074

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