Second-Order Regularity Estimates for Singular Schrödinger Equations on Convex Domains
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 int...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/216867 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |