Extremal Values of Half-Eigenvalues for -Laplacian with Weights in Balls
© Ping Yan. 2010
Received: 24 May 2010
Accepted: 21 October 2010
Published: 2 November 2010
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.
To access the full article, please see PDF.
This article is published under license to BioMed Central Ltd. 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.