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arXiv · 2505.23423

Doubling Inequality and Strong Unique Continuation for an Elliptic Transmission Problem

Tianrui Dai·Elisa Francini·Sergio Vessella
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Abstract

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.

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Tianrui Dai, Elisa Francini, Sergio Vessella. 2025-05-29. Doubling Inequality and Strong Unique Continuation for an Elliptic Transmission Problem. https://arxiv.org/abs/2505.23423

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