Singular solutions for complex second order elliptic equations and their application to time-harmonic diffuse optical tomography
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917629876240384 |
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| author | Curran, Jason Gaburro, Romina Nolan, Clifford |
| author_facet | Curran, Jason Gaburro, Romina Nolan, Clifford |
| contents | We construct singular solutions of a complex elliptic equation of second order, having an isolated singularity of any order. In particular, we extend results obtained for the real partial differential equation in divergence form by Alessandrini in 1990. Our solutions can be applied to the determination of the optical properties of an anisotropic medium in time-harmonic Diffuse Optical Tomography (DOT). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02987 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singular solutions for complex second order elliptic equations and their application to time-harmonic diffuse optical tomography Curran, Jason Gaburro, Romina Nolan, Clifford Analysis of PDEs We construct singular solutions of a complex elliptic equation of second order, having an isolated singularity of any order. In particular, we extend results obtained for the real partial differential equation in divergence form by Alessandrini in 1990. Our solutions can be applied to the determination of the optical properties of an anisotropic medium in time-harmonic Diffuse Optical Tomography (DOT). |
| title | Singular solutions for complex second order elliptic equations and their application to time-harmonic diffuse optical tomography |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.02987 |