Propagation of smallness and size estimate in the second order elliptic equation with discontinuous complex Lipschitz conductivity

2020/07/02 by Elisa Francini, Francini, Elisa, Sergio Vessella +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2007.01094

openalex publication_date 2020/07/02 · openalex created_date 2022/11/02 · openalex updated_date 2026/07/28

Abstract

In this paper, we would like to derive three-ball inequalities and propagation of smallness for the complex second order elliptic equation with discontinuous Lipschitz coefficients. As an application of such estimates, we study the size estimate problem by one pair of Cauchy data on the boundary. The main ingredient in the derivation of three-ball inequalities and propagation of smallness is a local Carleman proved in our recent paper [FVW].

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