Uniqueness of semilinear elliptic inverse problem (Q1774352)

Summary: We consider the uniqueness of the inverse problem for a semilinear elliptic differential equation with Dirichlet condition \[ -\Delta u+a(x,u)=0,\;x\in\Omega, \] \[ u|_{\partial \Omega}=g\in W^{2-1/p,p}(\partial \Omega). \] A necessary and sufficient condition for a unique solution is obtained. We improve the results obtained by \textit{V. Isakov} and \textit{J. Sylvester} [Commun. Pure Appl. Math. 47, No. 10, 1403--1410 (1994; Zbl 0817.35126)] for the same problem, replacing \(\Delta u\) by \(\sum c_{ij}\partial_{ij}u\).