Carleman estimate for complex second order elliptic operators with discontinuous Lipschitz coefficients

2020/01/13 by Francini, E., Vessella, S., Wang, J. -N. · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.04071

Abstract

In this paper, we derive a local Carleman estimate for the complex second order elliptic operator with Lipschitz coefficients having jump discontinuities. Combing the result in [BL] and the arguments in [DcFLVW], we present an elementary method to derive the Carleman estimate under the optimal regularity assumption on the coefficients.

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• Elliptic unique continuation below the Lipschitz threshold
• Doubling Inequality and Strong Unique Continuation for an Elliptic Transmission Problem

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