Doubling Inequality and Strong Unique Continuation for an Elliptic Transmission Problem
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910973746479104 |
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| author | Dai, Tianrui Francini, Elisa Vessella, Sergio |
| author_facet | Dai, Tianrui Francini, Elisa Vessella, Sergio |
| contents | We investigate the Strong Unique Continuation Property (SUCP) for elliptic equations with piecewise Lipschitz coefficients exhibiting jump discontinuities across a regular interface. We prove SUCP at the interface using a doubling inequality derived from a Carleman estimate with a singular weight. This result is intended as a first step toward solving the inverse problem of estimating the size of an unknown, merely measurable, inclusion inside a conductor from boundary measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23423 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Doubling Inequality and Strong Unique Continuation for an Elliptic Transmission Problem Dai, Tianrui Francini, Elisa Vessella, Sergio Analysis of PDEs We investigate the Strong Unique Continuation Property (SUCP) for elliptic equations with piecewise Lipschitz coefficients exhibiting jump discontinuities across a regular interface. We prove SUCP at the interface using a doubling inequality derived from a Carleman estimate with a singular weight. This result is intended as a first step toward solving the inverse problem of estimating the size of an unknown, merely measurable, inclusion inside a conductor from boundary measurements. |
| title | Doubling Inequality and Strong Unique Continuation for an Elliptic Transmission Problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.23423 |