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September/October 2015 A priori estimate for the first eigenvalue of the $p$-Laplacian
Ryuji Kajikiya
Differential Integral Equations 28(9/10): 1011-1028 (September/October 2015).

Abstract

We study the first eigenvalue of the $p$-Laplacian under the Dirichlet boundary condition. For a convex domain, we give an a priori estimate for the first eigenvalue in terms of the radius $d$ of the maximum ball contained in the domain. As a consequence, we prove that the first eigenvalue diverges to infinity as $p\to\infty$ if the domain is convex and $d\leq 1$. Moreover, we show that in the annulus domain $a < |x| < b$, the first eigenvalue diverges to infinity if $b-a\leq 2$ and converges to zero if $b-a>2$.

Citation

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Ryuji Kajikiya. "A priori estimate for the first eigenvalue of the $p$-Laplacian." Differential Integral Equations 28 (9/10) 1011 - 1028, September/October 2015.

Information

Published: September/October 2015
First available in Project Euclid: 23 June 2015

zbMATH: 1363.35096
MathSciNet: MR3360728

Subjects:
Primary: 35J20, 35J25, 35J92

Rights: Copyright © 2015 Khayyam Publishing, Inc.

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Vol.28 • No. 9/10 • September/October 2015
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