Second-Order Regularity Estimates for Singular Schrödinger Equations on Convex Domains - Xiangxing Tao (Abstract and Applied Analysis)
Let Ω⊂ℝn be a nonsmooth convex domain and let f be a distribution in the atomic Hardy space Hatp(Ω); we study the Schrödinger equations -div⁡(A∇u)+Vu=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 Lp 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.