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On the strict monotonicity of the first eigenvalue of the $p$-Laplacian on annuli | | T. V. Anoop
; Vladimir Bobkov
; Sarath Sasi
; | | Date: |
10 Nov 2016 | | Abstract: | Let $B_1$ be a ball in $mathbb{R}^N$ centred at the origin and $B_0$ be a
smaller ball compactly contained in $B_1$. For $pin(1, infty)$, using the
shape derivative method, we show that the first eigenvalue of the $p$-Laplacian
in annulus $B_1setminus overline{B_0}$ strictly decreases as the inner ball
moves towards the boundary of the outer ball. The analogous results for the
limit cases as $p o 1$ and $p o infty$ are also discussed. Using our main
result, further we prove the nonradiality of the eigenfunctions associated with
the points on the first nontrivial curve of the Fuv{c}ik spectrum of the
$p$-Laplacian on bounded radial domains. | | Source: | arXiv, 1611.3532 | | Services: | Forum | Review | PDF | Favorites | |
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