Existence of solutions to the Poisson equation in $L_p$-weighted spaces

Joanna Rencławowicz, and Wojciech M. Zajączkowski. "Existence of solutions to the Poisson equation in $L_p$-weighted spaces." Applicationes Mathematicae 37.1 (2010): 1-12. <http://eudml.org/doc/279914>.

@article{JoannaRencławowicz2010,
abstract = {We examine the Poisson equation with boundary conditions on a cylinder in a weighted space of $L_p$, p≥ 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 L₂ space.},
author = {Joanna Rencławowicz, Wojciech M. Zajączkowski},
journal = {Applicationes Mathematicae},
keywords = {Poisson equation; weighted Sobolev spaces; Neumann boundary-value problem; Dirichlet boundary-value problem},
language = {eng},
number = {1},
pages = {1-12},
title = {Existence of solutions to the Poisson equation in $L_p$-weighted spaces},
url = {http://eudml.org/doc/279914},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Joanna Rencławowicz
AU - Wojciech M. Zajączkowski
TI - Existence of solutions to the Poisson equation in $L_p$-weighted spaces
JO - Applicationes Mathematicae
PY - 2010
VL - 37
IS - 1
SP - 1
EP - 12
AB - We examine the Poisson equation with boundary conditions on a cylinder in a weighted space of $L_p$, p≥ 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 L₂ space.
LA - eng
KW - Poisson equation; weighted Sobolev spaces; Neumann boundary-value problem; Dirichlet boundary-value problem
UR - http://eudml.org/doc/279914
ER -