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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 216867, 10 pages
http://dx.doi.org/10.1155/2014/216867
Research Article

Second-Order Regularity Estimates for Singular Schrödinger Equations on Convex Domains

Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, China

Received 21 November 2013; Accepted 17 January 2014; Published 3 March 2014

Academic Editor: Chong Li

Copyright © 2014 Xiangxing Tao. 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

Let be a nonsmooth convex domain and let be a distribution in the atomic Hardy space ; we study the Schrödinger equations in with the singular potential and the nonsmooth coefficient matrix . We will show the existence of the Green function and establish the integrability of the second-order derivative of the solution to the Schrödinger equation on with the Dirichlet boundary condition for . Some fundamental pointwise estimates for the Green function are also given.