H\"older stability for a semilinear elliptic inverse problem

TL;DR

This paper improves the stability estimates for recovering nonlinear terms in semilinear elliptic equations from boundary data, achieving H"older stability with fewer measurements and less regular nonlinearities.

Contribution

It establishes a H"older stability estimate for the inverse problem, reducing the boundary measurements and regularity requirements compared to previous results.

Findings

H"older stability estimate proven

Fewer boundary measurements used

Applicable to less regular nonlinearities

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 H\"older 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.