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

作者：Kajikiya Ryuji^*

来源：Differential and Integral Equations, 2015, 28(9-10): 1011-1028.

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.

• 出版日期2015-10