On the Poisson equation in exterior domains

Authors : Werner VARNHORN

Pages : 134-140

Doi:10.33205/cma.1143800

View : 10 | Download : 7

Publication Date : 2022-09-15

Article Type : Research Paper

Abstract :We construct a solution of the Poisson equation in exterior domains $\Omega \subset \mathbb R^n,\;n \ge 2,$ in homogeneous Lebesgue spaces $L^{2,q}insert ignore into journalissuearticles values(\Omega);,;1 < q <\infty,$ 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