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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832561429334458368 |
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| author | Xiangxing Tao |
| author_facet | Xiangxing Tao |
| author_sort | Xiangxing Tao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-62d91ac7e4a24cc8aba8fd1998ccc1a9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-62d91ac7e4a24cc8aba8fd1998ccc1a92025-02-03T01:25:06ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/216867216867Second-Order Regularity Estimates for Singular Schrödinger Equations on Convex DomainsXiangxing Tao0Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, ChinaLet 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.http://dx.doi.org/10.1155/2014/216867 |
| spellingShingle | Xiangxing Tao Second-Order Regularity Estimates for Singular Schrödinger Equations on Convex Domains Abstract and Applied Analysis |
| title | Second-Order Regularity Estimates for Singular Schrödinger Equations on Convex Domains |
| title_full | Second-Order Regularity Estimates for Singular Schrödinger Equations on Convex Domains |
| title_fullStr | Second-Order Regularity Estimates for Singular Schrödinger Equations on Convex Domains |
| title_full_unstemmed | Second-Order Regularity Estimates for Singular Schrödinger Equations on Convex Domains |
| title_short | Second-Order Regularity Estimates for Singular Schrödinger Equations on Convex Domains |
| title_sort | second order regularity estimates for singular schrodinger equations on convex domains |
| url | http://dx.doi.org/10.1155/2014/216867 |
| work_keys_str_mv | AT xiangxingtao secondorderregularityestimatesforsingularschrodingerequationsonconvexdomains |