Abstract and Applied Analysis

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

Xiangxing Tao

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

First available in Project Euclid: 6 October 2014

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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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