Bulletin of the
Korean Mathematical Society BKMS

Choi, Kim and Lee have proposed a new asymptotic Dirichlet problem for harmonic functionvia the rough isometry on a certain class of Riemannian manifolds, and they proved that this problem is solvable for naturally defined class of functions.In this paper, we generalize their result in the setting of the Schr\"odinger operator with suitable potential.

Keywords: Rough isometry, asymptotic boundary, boundary at infinity, Dirichlet problem, Schrodinger operator, net, Poincar\'e inequality, Sobolev inequality

MSC numbers: 31C20, 53C21, 58G03, 58G20