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The ∞-Laplacian First Eigenvalue Problem

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Free Boundary Problems

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 154))

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Abstract

We review some results about the first eigenvalue of the infinity Laplacian operator and its first eigenfunctions in a general norm context. Those results are obtained in collaboration with several authors: V. Ferone, P. Juutinen and B. Kawohl (see [BFK], [BK1], [BJK] and [BK2]). In Section 5 we make some remarks on the simplicity of the first eigenvalue of Δ∞: this will be the object of a joint work with A. Wagner (see [BW]).

This work was completed with the support of the research project Calcolo delle Variazioni e Teoria Geometrica della Misura.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Parma, Via Parco delle Scienze, 53/A, I-43100, Parma, Italy

    Marino Belloni

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  1. Marino Belloni
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Editors and Affiliations

  1. Departamento de Matemática Faculdade de Ciências e Tecnologia, Universidade de Coimbra, Apartado 3008, 3001-454, Coimbra, Portugal

    Isabel Narra Figueiredo

  2. Universidade de Lisboa / CMAF, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal

    José Francisco Rodrigues

  3. Departamento de Matemática, Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    Lisa Santos

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Belloni, M. (2006). The ∞-Laplacian First Eigenvalue Problem. In: Figueiredo, I.N., Rodrigues, J.F., Santos, L. (eds) Free Boundary Problems. International Series of Numerical Mathematics, vol 154. Birkhäuser, Basel. https://doi.org/10.1007/978-3-7643-7719-9_9

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