Nonlinear Kato Class and Unique Continuation of Eigenfunctions for p-Laplacian Operator - René Erlín Castillo; Julio C. Ramos Fernández (Journal of Function Spaces and Applications)
We study some basic properties of nonlinear Kato class Mp(ℝn) and M~p(ℝn), respectively, for 1<p<n. Also, we study the problem -div(|∇u|p-2∇u)+V|u|p-2u=0 in Ω, where Ω is a bounded domain in ℝn 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).