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Journal of Function Spaces and Applications
Volume 2013, Article ID 512050, 7 pages
http://dx.doi.org/10.1155/2013/512050
Research Article

Nonlinear Kato Class and Unique Continuation of Eigenfunctions for -Laplacian Operator

1Departamento de Matemáticas, Universidad Nacional de Colombia, Apartado, 360354 Bogotá, Colombia
2Departamento de Matemáticas, Universidad de Oriente, Cumaná 6101 Estado Sucre, Venezuela

Received 25 April 2013; Revised 27 August 2013; Accepted 28 August 2013

Academic Editor: Janusz Matkowski

Copyright © 2013 René Erlín Castillo and Julio C. Ramos Fernández. 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

We study some basic properties of nonlinear Kato class and respectively, for Also, we study the problem in where is a bounded domain in and the weight function is assumed to be not equivalent to zero and lies in , in the case where . Finally, we establish the strong unique continuation property of the eigenfunction for the -Laplacian operator in the case where .