On the Poisson equation in exterior domains
Authors : Werner Varnhorn
Pages : 134-140
Doi:10.33205/cma.1143800
View : 11 | Download : 6
Publication Date : 2022-09-15
Article Type : Research
Abstract :We construct a solution of the Poisson equation in exterior domains $\Omega \subset \mathbb R^n,\;n \ge 2,$ in homogeneous Lebesgue spaces $L^{2,q}(\Omega),;1 < q <\infty,$ with methods of potential theory and integral equations. We investigate the corresponding null spaces and prove that its dimensions is equal to $n+1$ independent of $q$.Keywords : Poisson equation, potential theory, homogeneous Lebesgue spaces