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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.