Hölder stability for a semilinear elliptic inverse problem

2022/06/14 by Choulli, Mourad
#35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.06746

Abstract

We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually that we have Hölder stability estimate with less boundary measurents and less regular nonlinearities. We establish our stability inequality by following the same method as in [4]. This method consists in constructing special solutions vanishing at a subboundary of the domain.

Related

• Stable Determination and Reconstruction of a Quasilinear Term in an Elliptic Equation
• Stability inequality for a semilinear elliptic inverse problem
• Stable determination of the nonlinear term in a quasilinear elliptic equation by boundary measurements
• Inverse problems for semilinear elliptic equations with low regularity
• Hölder regularity of stable solutions to semilinear elliptic equations up to ℝ⁹: full quantitative proofs