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

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  • Xiangxing Tao

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.

Suggested Citation

  • Xiangxing Tao, 2014. "Second-Order Regularity Estimates for Singular Schrödinger Equations on Convex Domains," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, March.
    • Handle: RePEc:hin:jnlaaa:216867
    DOI: 10.1155/2014/216867
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