p-Laplacian operator with potential in generalized Morrey Spaces

2023/08/08 by Castillo, René Erlin, Chaparro, Héctor Camilo
#26D10 #35J05 #46E30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.04049

Abstract

We study some basic properties of generalized Morrey spaces M^p,ϕ(\R^d). Also, the problem -div(|∇ u|^p-2∇ u)+V|u|^p-2u=0 in Ω, where Ω is a bounded open set in \R^d, and potential V is assumed to be not equivalent to zero and lies in M^p,ϕ(Ω), is studied. Finally, we establish the strong unique continuation for the p-Laplace operator in the case V\inM^p,ϕ(\R^d).

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