An Inverse Problem with Partial Neumann Data and $L^{n/2}$ Potentials
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866909574348406784 |
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| author | Busch, Leonard Tzou, Leo |
| author_facet | Busch, Leonard Tzou, Leo |
| contents | We consider a partial data inverse problem with unbounded potentials. Rather than rely on functional analytic arguments or Carleman estimates, we construct an explicit Green's function with which we construct complex geometric optics (CGO) solutions and show unique determinability of potentials in $L^{n/2}$ for the Schrödinger equation with partial Neumann data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04983 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Inverse Problem with Partial Neumann Data and $L^{n/2}$ Potentials Busch, Leonard Tzou, Leo Analysis of PDEs We consider a partial data inverse problem with unbounded potentials. Rather than rely on functional analytic arguments or Carleman estimates, we construct an explicit Green's function with which we construct complex geometric optics (CGO) solutions and show unique determinability of potentials in $L^{n/2}$ for the Schrödinger equation with partial Neumann data. |
| title | An Inverse Problem with Partial Neumann Data and $L^{n/2}$ Potentials |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2312.04983 |