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2014 Second-Order Regularity Estimates for Singular Schrödinger Equations on Convex Domains
Xiangxing Tao
Abstr. Appl. Anal. 2014(SI57): 1-10 (2014). DOI: 10.1155/2014/216867

Abstract

Let Ω n be a nonsmooth convex domain and let f be a distribution in the atomic Hardy space H a t p ( Ω ) ; we study the Schrödinger equations - div ( A u ) + V u = f in Ω with the singular potential V and the nonsmooth coefficient matrix A . We will show the existence of the Green function and establish the L p integrability of the second-order derivative of the solution to the Schrödinger equation on Ω with the Dirichlet boundary condition for n / ( n + 1 ) < p 2 . Some fundamental pointwise estimates for the Green function are also given.

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Xiangxing Tao. "Second-Order Regularity Estimates for Singular Schrödinger Equations on Convex Domains." Abstr. Appl. Anal. 2014 (SI57) 1 - 10, 2014. https://doi.org/10.1155/2014/216867

Information

Published: 2014
First available in Project Euclid: 6 October 2014

zbMATH: 1298.26089
MathSciNet: MR3178855
Digital Object Identifier: 10.1155/2014/216867

Rights: Copyright © 2014 Hindawi

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Vol.2014 • No. SI57 • 2014
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