| Issue |
ESAIM: COCV
Volume 21, Number 1, January-March 2015
|
|
|---|---|---|
| Page(s) | 60 - 72 | |
| DOI | https://doi.org/10.1051/cocv/2014017 | |
| Published online | 17 October 2014 | |
On the Faber–Krahn inequality for the Dirichlet p-Laplacian∗
1 Indian Institute of Science Education and Research, Pune,
India.
anisa@iiserpune.ac.in
2 Departamento de Matemática, Univ. de Concepción, Concepción,
Chile.
rmahadevan@udec.cl;franciscotoledo@udec.cl
Received:
20
July
2013
Revised:
28
February
2014
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.
Mathematics Subject Classification: 35B06 / 35B51 / 35J92 / 35P30 / 49Q20
Key words: Symmetry / moving plane method / comparison principles / boundary point lemma
© EDP Sciences, SMAI 2014
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