Abstract and Applied Analysis
Volume 2012 (2012), Article ID 453891, 29 pages
http://dx.doi.org/10.1155/2012/453891
Research Article

Criteria of Wiener Type for Minimally Thin Sets and Rarefied Sets Associated with the Stationary Schrödinger Operator in a Cone

Pinhong Long, Zhiqiang Gao, and Guantie Deng

Laboratory of Mathematics and Complex Systems, School of Mathematical Science, Beijing Normal University, Beijing 100875, China

Received 8 April 2012; Accepted 18 June 2012

Academic Editor: Ondřej Došlý

Copyright © 2012 Pinhong Long et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give some criteria for a-minimally thin sets and a-rarefied sets associated with the stationary Schrödinger operator at a fixed Martin boundary point or ∞ with respect to a cone. Moreover, we show that a positive superfunction on a cone behaves regularly outside an a-rarefied set. Finally we illustrate the relation between the a-minimally thin set and the a-rarefied set in a cone.