An inverse problem originating from magnetohydrodynamics. III: Domains with corners of arbitrary angles. (English) Zbl 0853.76093

Beretta, Elena; Vogelius, Michael

Asymptotic Anal. 11, No. 3, 289-315 (1995).

Summary: We seek to identify the nonlinearity of the semilinear elliptic equation \(\Delta u= -f(u)\leq 0\) from boundary measurements of the normal flux corresponding to homogeneous Dirichlet data. The possibility of such identification depends crucially on the shape of the domain. In this paper we prove that identification of an analytic function \(f\) is (generically) possible if the domain has a proper corner. This result significantly extends an earlier result obtained by the authors [Arch. Ration. Mech. Anal. 115, No. 2, 137-152 (1991; Zbl 0732.76096)], by almost entirely eliminating the restrictions imposed on the size of the angle of the corner.

MSC:

76W05	Magnetohydrodynamics and electrohydrodynamics
35R30	Inverse problems for PDEs

Keywords:

semilinear elliptic equation; homogeneous Dirichlet data; identification; analytic function