$p$-Laplacian operator with potential in generalized Morrey Spaces
We study some basic properties of generalized Morrey spaces $\mathcal{M}^{p,ϕ}(\R^{d})$. Also, the problem $-\mbox{div}(|\nabla u|^{p-2}\nabla u)+V|u|^{p-2}u=0$ 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 $\mathcal{M}^{p,ϕ}(Ω)$, is studied. Finally, we establish the strong unique continuation for the $p$-Laplace operator in the case $V\in\mathcal{M}^{p,ϕ}(\R^d)$.
math.AP↗