Optimal ground state energy of two-phase conductors
We consider the problem of distributing two conducting materials in a ball with fixed proportion in order to minimize the first eigenvalue of a Dirichlet operator. It was conjectured that the optimal distribution consists of putting the material with the highest conductivity in a ball around the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-08-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/171/abstr.html |
| _version_ | 1818218624203096064 |
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| author | Abbasali Mohammadi Mohsen Yousefnezhad |
| author_facet | Abbasali Mohammadi Mohsen Yousefnezhad |
| author_sort | Abbasali Mohammadi |
| collection | DOAJ |
| description | We consider the problem of distributing two conducting materials in a
ball with fixed proportion in order to minimize the first eigenvalue
of a Dirichlet operator. It was conjectured that the optimal
distribution consists of putting the material with the highest conductivity
in a ball around the center. In this paper, we show that the conjecture
is false for all dimensions greater than or equal to two. |
| first_indexed | 2024-12-12T07:26:43Z |
| format | Article |
| id | doaj.art-1bbb878c88644f84939217eb878bff03 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-12T07:26:43Z |
| publishDate | 2014-08-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-1bbb878c88644f84939217eb878bff032022-12-22T00:33:08ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912014-08-012014171,18Optimal ground state energy of two-phase conductorsAbbasali Mohammadi0Mohsen Yousefnezhad1 Yasouj Univ., Yasouj, Iran Sharif Univ. of Technology, Tehran, Iran We consider the problem of distributing two conducting materials in a ball with fixed proportion in order to minimize the first eigenvalue of a Dirichlet operator. It was conjectured that the optimal distribution consists of putting the material with the highest conductivity in a ball around the center. In this paper, we show that the conjecture is false for all dimensions greater than or equal to two.http://ejde.math.txstate.edu/Volumes/2014/171/abstr.htmlEigenvalue optimizationtwo-phase conductorsrearrangementsBessel function |
| spellingShingle | Abbasali Mohammadi Mohsen Yousefnezhad Optimal ground state energy of two-phase conductors Electronic Journal of Differential Equations Eigenvalue optimization two-phase conductors rearrangements Bessel function |
| title | Optimal ground state energy of two-phase conductors |
| title_full | Optimal ground state energy of two-phase conductors |
| title_fullStr | Optimal ground state energy of two-phase conductors |
| title_full_unstemmed | Optimal ground state energy of two-phase conductors |
| title_short | Optimal ground state energy of two-phase conductors |
| title_sort | optimal ground state energy of two phase conductors |
| topic | Eigenvalue optimization two-phase conductors rearrangements Bessel function |
| url | http://ejde.math.txstate.edu/Volumes/2014/171/abstr.html |
| work_keys_str_mv | AT abbasalimohammadi optimalgroundstateenergyoftwophaseconductors AT mohsenyousefnezhad optimalgroundstateenergyoftwophaseconductors |