An inverse boundary-value problem for semilinear elliptic equations
We show that in dimension two or greater, a certain equivalence class of the scalar coefficient $a(x,u)$ of the semilinear elliptic equation $Delta u,+a(x,u)=0$ is uniquely determined by the Dirichlet to Neumann map of the equation on a bounded domain with smooth boundary. We also show that the...
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| Format: | Article |
| Language: | English |
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Texas State University
2010-03-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2010/37/abstr.html |
| _version_ | 1811287538203099136 |
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| author | Ziqi Sun |
| author_facet | Ziqi Sun |
| author_sort | Ziqi Sun |
| collection | DOAJ |
| description | We show that in dimension two or greater, a certain equivalence class of the scalar coefficient $a(x,u)$ of the semilinear elliptic equation $Delta u,+a(x,u)=0$ is uniquely determined by the Dirichlet to Neumann map of the equation on a bounded domain with smooth boundary. We also show that the coefficient $a(x,u)$ can be determined by the Dirichlet to Neumann map under some additional hypotheses. |
| first_indexed | 2024-04-13T03:20:16Z |
| format | Article |
| id | doaj.art-f32d62d4bc774849bd259ca323c3c5e6 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-13T03:20:16Z |
| publishDate | 2010-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-f32d62d4bc774849bd259ca323c3c5e62022-12-22T03:04:48ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912010-03-01201037,15An inverse boundary-value problem for semilinear elliptic equationsZiqi SunWe show that in dimension two or greater, a certain equivalence class of the scalar coefficient $a(x,u)$ of the semilinear elliptic equation $Delta u,+a(x,u)=0$ is uniquely determined by the Dirichlet to Neumann map of the equation on a bounded domain with smooth boundary. We also show that the coefficient $a(x,u)$ can be determined by the Dirichlet to Neumann map under some additional hypotheses.http://ejde.math.txstate.edu/Volumes/2010/37/abstr.htmlInverse ProblemDirichlet to Neumann map |
| spellingShingle | Ziqi Sun An inverse boundary-value problem for semilinear elliptic equations Electronic Journal of Differential Equations Inverse Problem Dirichlet to Neumann map |
| title | An inverse boundary-value problem for semilinear elliptic equations |
| title_full | An inverse boundary-value problem for semilinear elliptic equations |
| title_fullStr | An inverse boundary-value problem for semilinear elliptic equations |
| title_full_unstemmed | An inverse boundary-value problem for semilinear elliptic equations |
| title_short | An inverse boundary-value problem for semilinear elliptic equations |
| title_sort | inverse boundary value problem for semilinear elliptic equations |
| topic | Inverse Problem Dirichlet to Neumann map |
| url | http://ejde.math.txstate.edu/Volumes/2010/37/abstr.html |
| work_keys_str_mv | AT ziqisun aninverseboundaryvalueproblemforsemilinearellipticequations AT ziqisun inverseboundaryvalueproblemforsemilinearellipticequations |