Existence of solutions to the Poisson equation in $L_p$-weighted spaces
Volume 37 / 2010
Applicationes Mathematicae 37 (2010), 1-12
MSC: Primary 35J05; Secondary 31A30, 35J25.
DOI: 10.4064/am37-1-1
Abstract
We examine the Poisson equation with boundary conditions on a cylinder in a weighted space of $L_p$, $ p\geq 3$, type. The weight is a positive power of the distance from a distinguished plane. To prove the existence of solutions we use our result on existence in a weighted $L_2$ space.
