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 |
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doaj-f32d62d4bc774849bd259ca323c3c5e62020-11-24T23:29:29ZengTexas 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ziqi Sun |
| spellingShingle |
Ziqi Sun An inverse boundary-value problem for semilinear elliptic equations Electronic Journal of Differential Equations Inverse Problem Dirichlet to Neumann map |
| author_facet |
Ziqi Sun |
| author_sort |
Ziqi Sun |
| title |
An inverse boundary-value problem for semilinear elliptic equations |
| title_short |
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_sort |
inverse boundary-value problem for semilinear elliptic equations |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2010-03-01 |
| 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. |
| 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 |
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1725545367802478592 |