Quasilinear differential equations in exterior domains with nonlinear boundary conditions and application
We investigate the existence of weak solutions to a class of quasilinear elliptic equations with nonlinear Neumann boundary conditions in exterior domains. Problems of this kind arise in various areas of science and technology. An important model case related to the initial data problem in gener...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2009-10-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2009/138/abstr.html |
| _version_ | 1818066999471767552 |
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| author | Nicolae Tarfulea Dumitru Motreanu |
| author_facet | Nicolae Tarfulea Dumitru Motreanu |
| author_sort | Nicolae Tarfulea |
| collection | DOAJ |
| description | We investigate the existence of weak solutions to a class of quasilinear elliptic equations with nonlinear Neumann boundary conditions in exterior domains. Problems of this kind arise in various areas of science and technology. An important model case related to the initial data problem in general relativity is presented. As an application of our main result, we deduce the existence of the conformal factor for the Hamiltonian constraint in general relativity in the presence of multiple black holes. We also give a proof for uniqueness in this case. |
| first_indexed | 2024-12-10T15:16:42Z |
| format | Article |
| id | doaj.art-9617a43220184084ad89e9004493d5f6 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-10T15:16:42Z |
| publishDate | 2009-10-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-9617a43220184084ad89e9004493d5f62022-12-22T01:43:46ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912009-10-012009138,113Quasilinear differential equations in exterior domains with nonlinear boundary conditions and applicationNicolae TarfuleaDumitru MotreanuWe investigate the existence of weak solutions to a class of quasilinear elliptic equations with nonlinear Neumann boundary conditions in exterior domains. Problems of this kind arise in various areas of science and technology. An important model case related to the initial data problem in general relativity is presented. As an application of our main result, we deduce the existence of the conformal factor for the Hamiltonian constraint in general relativity in the presence of multiple black holes. We also give a proof for uniqueness in this case.http://ejde.math.txstate.edu/Volumes/2009/138/abstr.htmlQuasilinear equationexterior domaingeneral relativitynonlinear boundary conditionsinitial data problemconformal factor |
| spellingShingle | Nicolae Tarfulea Dumitru Motreanu Quasilinear differential equations in exterior domains with nonlinear boundary conditions and application Electronic Journal of Differential Equations Quasilinear equation exterior domain general relativity nonlinear boundary conditions initial data problem conformal factor |
| title | Quasilinear differential equations in exterior domains with nonlinear boundary conditions and application |
| title_full | Quasilinear differential equations in exterior domains with nonlinear boundary conditions and application |
| title_fullStr | Quasilinear differential equations in exterior domains with nonlinear boundary conditions and application |
| title_full_unstemmed | Quasilinear differential equations in exterior domains with nonlinear boundary conditions and application |
| title_short | Quasilinear differential equations in exterior domains with nonlinear boundary conditions and application |
| title_sort | quasilinear differential equations in exterior domains with nonlinear boundary conditions and application |
| topic | Quasilinear equation exterior domain general relativity nonlinear boundary conditions initial data problem conformal factor |
| url | http://ejde.math.txstate.edu/Volumes/2009/138/abstr.html |
| work_keys_str_mv | AT nicolaetarfulea quasilineardifferentialequationsinexteriordomainswithnonlinearboundaryconditionsandapplication AT dumitrumotreanu quasilineardifferentialequationsinexteriordomainswithnonlinearboundaryconditionsandapplication |