A PRIORI ESTIMATE FOR THE FIRST EIGENVALUE OF THE p-LAPLACIAN

被引:0
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作者
Kajikiya, Ryuji [1 ]
机构
[1] Saga Univ, Fac Sci & Engn, Dept Math, Saga 8408502, Japan
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中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 -> infinity if the domain is convex and d <= 1. Moreover, we show that in the annulus domain a < vertical bar x vertical bar < b, the first eigenvalue diverges to infinity if b - a <= 2 and converges to zero if b - a > 2.
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页码:1011 / 1028
页数:18
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