Recovering nonsmooth coefficients for higher-order perturbations of a polyharmonic operator
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916550175358976 |
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| author | Brown, Russell M. Gauthier, Landon Faraco, Daniel |
| author_facet | Brown, Russell M. Gauthier, Landon Faraco, Daniel |
| contents | We consider an inverse problem for a higher order elliptic operator where the principal part is the polyharmonic operator $(-Δ)^m$ with $ m \geq 2$. We show that the map from the coefficients to a certain bilinear form is injective. We have a particular focus on obtaining these results under lower regularity on the coefficients. It is known that knowledge of this bilinear form is equivalent to a knowledge of a Dirichlet to Neumann map or the Cauchy data for solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01858 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Recovering nonsmooth coefficients for higher-order perturbations of a polyharmonic operator Brown, Russell M. Gauthier, Landon Faraco, Daniel Analysis of PDEs 35R30, 35J40 We consider an inverse problem for a higher order elliptic operator where the principal part is the polyharmonic operator $(-Δ)^m$ with $ m \geq 2$. We show that the map from the coefficients to a certain bilinear form is injective. We have a particular focus on obtaining these results under lower regularity on the coefficients. It is known that knowledge of this bilinear form is equivalent to a knowledge of a Dirichlet to Neumann map or the Cauchy data for solutions. |
| title | Recovering nonsmooth coefficients for higher-order perturbations of a polyharmonic operator |
| topic | Analysis of PDEs 35R30, 35J40 |
| url | https://arxiv.org/abs/2501.01858 |