On the scattered field generated by a ball inhomogeneity of constant index in dimension three
We consider the solution of a scalar Helmholtz equation where the potential (or index) takes two positive values, one inside a ball of radius $\eps$ and another one outside. In this short paper, we report that the results recently obtained in the two dimensional case in [1] can be easily extended to...
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| Format: | Journal article |
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American Mathematical Society
2012
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| _version_ | 1797051042561523712 |
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| author | Capdeboscq, Y Leadbetter, G Parker, A |
| author_facet | Capdeboscq, Y Leadbetter, G Parker, A |
| author_sort | Capdeboscq, Y |
| collection | OXFORD |
| description | We consider the solution of a scalar Helmholtz equation where the potential (or index) takes two positive values, one inside a ball of radius $\eps$ and another one outside. In this short paper, we report that the results recently obtained in the two dimensional case in [1] can be easily extended to three dimensions. In particular, we provide sharp estimates of the size of the scattered field caused by this ball inhomogeneity, for any frequencies and any contrast. We also provide a broadband estimate, that is, a uniform bound for the scattered field for any contrast, and any frequencies outside of a set which tends to zero with $\eps$. |
| first_indexed | 2024-03-06T18:14:11Z |
| format | Journal article |
| id | oxford-uuid:040c2388-99ff-4604-ba1d-03eb26e5f436 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:14:11Z |
| publishDate | 2012 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:040c2388-99ff-4604-ba1d-03eb26e5f4362022-03-26T08:49:45ZOn the scattered field generated by a ball inhomogeneity of constant index in dimension threeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:040c2388-99ff-4604-ba1d-03eb26e5f436Symplectic Elements at OxfordAmerican Mathematical Society2012Capdeboscq, YLeadbetter, GParker, AWe consider the solution of a scalar Helmholtz equation where the potential (or index) takes two positive values, one inside a ball of radius $\eps$ and another one outside. In this short paper, we report that the results recently obtained in the two dimensional case in [1] can be easily extended to three dimensions. In particular, we provide sharp estimates of the size of the scattered field caused by this ball inhomogeneity, for any frequencies and any contrast. We also provide a broadband estimate, that is, a uniform bound for the scattered field for any contrast, and any frequencies outside of a set which tends to zero with $\eps$. |
| spellingShingle | Capdeboscq, Y Leadbetter, G Parker, A On the scattered field generated by a ball inhomogeneity of constant index in dimension three |
| title | On the scattered field generated by a ball inhomogeneity of constant
index in dimension three |
| title_full | On the scattered field generated by a ball inhomogeneity of constant
index in dimension three |
| title_fullStr | On the scattered field generated by a ball inhomogeneity of constant
index in dimension three |
| title_full_unstemmed | On the scattered field generated by a ball inhomogeneity of constant
index in dimension three |
| title_short | On the scattered field generated by a ball inhomogeneity of constant
index in dimension three |
| title_sort | on the scattered field generated by a ball inhomogeneity of constant index in dimension three |
| work_keys_str_mv | AT capdeboscqy onthescatteredfieldgeneratedbyaballinhomogeneityofconstantindexindimensionthree AT leadbetterg onthescatteredfieldgeneratedbyaballinhomogeneityofconstantindexindimensionthree AT parkera onthescatteredfieldgeneratedbyaballinhomogeneityofconstantindexindimensionthree |