## Abstract and Applied Analysis

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

Xiangxing Tao

#### Abstract

Let $\mathrm{\Omega }\subset {\Bbb R}^{n}$ be a nonsmooth convex domain and let $f$ be a distribution in the atomic Hardy space ${H}_{at}^{p}(\mathrm{\Omega })$; we study the Schrödinger equations $-\mathrm{div}(A\nabla u)+Vu=f$ in $\mathrm{\Omega }$ 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 $\mathrm{\Omega }$ with the Dirichlet boundary condition for $n/(n+\mathrm{1}). 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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