Dirichlet problem for the Schrödinger operator on a cone
1 Department of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, 450002, P.R. China
2 School of Mathematical Science, Laboratory of Mathematics and Complex Systems, MOE Beijing Normal University, Beijing, 100875, P.R. China
Boundary Value Problems 2012, 2012:59 doi:10.1186/1687-2770-2012-59Published: 18 June 2012
In this article, a solution of the Dirichlet problem for the Schrödinger operator on a cone is constructed by the generalized Poisson integral with a slowly growing continuous boundary function. A solution of the Poisson integral for any continuous boundary function is also given explicitly by the Poisson integral with the generalized Poisson kernel depending on this boundary function.
MSC: 31B05, 31B10.