H\"older stability for a semilinear elliptic inverse problem

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.