The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz
We investigate the Dirichlet problem related to linear elliptic second-order partial differential operators with smooth coefficients in divergence form in bounded connected domains of Rm (m≥3) with Lyapunov boundary. In particular, we show how to represent the solution in terms of a simple layer pot...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/276810 |
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| author | Alberto Cialdea Vita Leonessa Angelica Malaspina |
| author_facet | Alberto Cialdea Vita Leonessa Angelica Malaspina |
| author_sort | Alberto Cialdea |
| collection | DOAJ |
| description | We investigate the Dirichlet problem related to linear elliptic second-order partial differential operators with smooth coefficients in divergence form in bounded connected domains of Rm (m≥3) with Lyapunov boundary. In particular, we show how to represent the solution in terms of a simple layer potential. We use an indirect boundary integral method hinging on the theory of reducible operators and the theory of differential forms. |
| format | Article |
| id | doaj-art-5253da3ae646412fabbef5e404c5e3cd |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5253da3ae646412fabbef5e404c5e3cd2025-02-03T01:03:45ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/276810276810The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential AnsatzAlberto Cialdea0Vita Leonessa1Angelica Malaspina2Department of Mathematics, Computer Science and Economics, University of Basilicata, Viale dell'Ateneo Lucano 10, 85100 Potenza, ItalyDepartment of Mathematics, Computer Science and Economics, University of Basilicata, Viale dell'Ateneo Lucano 10, 85100 Potenza, ItalyDepartment of Mathematics, Computer Science and Economics, University of Basilicata, Viale dell'Ateneo Lucano 10, 85100 Potenza, ItalyWe investigate the Dirichlet problem related to linear elliptic second-order partial differential operators with smooth coefficients in divergence form in bounded connected domains of Rm (m≥3) with Lyapunov boundary. In particular, we show how to represent the solution in terms of a simple layer potential. We use an indirect boundary integral method hinging on the theory of reducible operators and the theory of differential forms.http://dx.doi.org/10.1155/2015/276810 |
| spellingShingle | Alberto Cialdea Vita Leonessa Angelica Malaspina The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz Abstract and Applied Analysis |
| title | The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz |
| title_full | The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz |
| title_fullStr | The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz |
| title_full_unstemmed | The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz |
| title_short | The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz |
| title_sort | dirichlet problem for second order divergence form elliptic operators with variable coefficients the simple layer potential ansatz |
| url | http://dx.doi.org/10.1155/2015/276810 |
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