New global logarithmic stability of the Cauchy problem for elliptic equations

2019/03/04 by Mourad Choulli, Choulli, Mourad
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1903.01136

openalex publication_date 2019/03/04 · openalex created_date 2019/03/11 · openalex updated_date 2026/07/28

Abstract

In this short paper we prove a global logarithmic stability of the Cauchy problem for H 2-solutions of an anisotropic elliptic equation in a Lip-schitz domain. The result we obtained is based on tools borrowed from the existing technics to establish stability estimate for the Cauchy problem [4] (see also [1]) combined with tools we already used in [6] to study an inverse medium problem.

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