Existence of solutions to the Poisson equation in $L_2$-weighted spaces
Volume 37 / 2010
Applicationes Mathematicae 37 (2010), 309-323
MSC: Primary 35J05; Secondary 31A30, 35J25.
DOI: 10.4064/am37-3-3
Abstract
We consider the Poisson equation with the Dirichlet and the Neumann boundary conditions in weighted Sobolev spaces. The weight is a positive power of the distance to a distinguished plane. We prove the existence of solutions in a suitably defined weighted space.
