Open Access Research Article

Extremal Values of Half-Eigenvalues for -Laplacian with Weights in Balls

Ping Yan

Author Affiliations

Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Boundary Value Problems 2010, 2010:690342  doi:10.1155/2010/690342


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Received:24 May 2010
Accepted:21 October 2010
Published:2 November 2010

© 2010 Ping Yan.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For one-dimensional -Laplacian with weights in balls, we are interested in the extremal values of the th positive half-eigenvalues associated with Dirichlet, Neumann, and generalized periodic boundary conditions, respectively. It will be shown that the extremal value problems for half-eigenvalues are equivalent to those for eigenvalues, and all these extremal values are given by some best Sobolev constants.

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