Abstract and Applied Analysis

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

Xiangxing Tao

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 216867, 10 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607613

Digital Object Identifier
doi:10.1155/2014/216867

Mathematical Reviews number (MathSciNet)
MR3178855

Zentralblatt MATH identifier
1298.26089

Citation

Tao, Xiangxing. Second-Order Regularity Estimates for Singular Schrödinger Equations on Convex Domains. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 216867, 10 pages. doi:10.1155/2014/216867. https://projecteuclid.org/euclid.aaa/1412607613


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