Nonlinear Kato Class and Unique Continuation of Eigenfunctions for p-Laplacian Operator. (1st October 2013)

• Record Type: Journal Article
• Authors: Castillo, René Erlín; Ramos Fernández, Julio C.
• Other Names: Matkowski Janusz Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2013(2013)
• Publication Date: 2013-10-01
• Subjects: Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2013/512050
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : We study some basic properties of nonlinear Kato class M p ( ℝ n ) and M ~ p ( ℝ n ), respectively, for 1 < p < n . Also, we study the problem - d i v ( | ∇ u | p - 2 ∇ u ) + V | u | p - 2 u = 0 in Ω, where Ω is a bounded domain in ℝ n and the weight function V is assumed to be not equivalent to zero and lies in M ~ p ( Ω ), in the case where p < n . Finally, we establish the strong unique continuation property of the eigenfunction for the p -Laplacian operator in the case where V ∈ M ~ p ( Ω ) .