Nonlinear Kato Class and Unique Continuation of Eigenfunctions for p-Laplacian Operator. (1st October 2013) - Castillo, René Erlín; Ramos Fernández, Julio C.
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 ) .