Geodesic
On the Faber–Krahn inequality for the Dirichlet p-Laplacian
Chorwadwala, Anisa M.H.1 ; Mahadevan, Rajesh2  ; Toledo, Francisco2
1 Indian Institute of Science Education and Research, Pune, India.
2 Departamento de Matemática, Univ. de Concepción, Concepción, Chile.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 1, pp. 60-72

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A famous conjecture made by Lord Rayleigh is the following: “The first eigenvalue of the Laplacian on an open domain of given measure with Dirichlet boundary conditions is minimum when the domain is a ball and only when it is a ball”. This conjecture was proved simultaneously and independently by Faber [G. Faber, Beweiss dass unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförfegige den leifsten Grundton gibt. Sitz. bayer Acad. Wiss. (1923) 169–172] and Krahn [E. Krahn, Über eine von Rayleigh formulierte Minimaleigenschaftdes Kreises. Math. Ann. 94 (1924) 97–100.]. We shall deal with the p-Laplacian version of this theorem.

Reçu le :
DOI : 10.1051/cocv/2014017
Classification : 35B06, 35B51, 35J92, 35P30, 49Q20
Keywords: Symmetry, moving plane method, comparison principles, boundary point lemma

Chorwadwala, Anisa M.H. 1 ; Mahadevan, Rajesh 2 ; Toledo, Francisco 2

1 Indian Institute of Science Education and Research, Pune, India.
2 Departamento de Matemática, Univ. de Concepción, Concepción, Chile. 
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Chorwadwala, Anisa M.H.; Mahadevan, Rajesh; Toledo, Francisco. On the Faber–Krahn inequality for the Dirichlet $p$-Laplacian. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 1, pp. 60-72. doi: 10.1051/cocv/2014017

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