Doubling Inequality and Strong Unique Continuation for an Elliptic Transmission Problem
Analysis of PDEs
2025-05-30 v1
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.
Keywords
Cite
@article{arxiv.2505.23423,
title = {Doubling Inequality and Strong Unique Continuation for an Elliptic Transmission Problem},
author = {Tianrui Dai and Elisa Francini and Sergio Vessella},
journal= {arXiv preprint arXiv:2505.23423},
year = {2025}
}