Some Aspects of the Boundary Trace Problem for Solutions of Nonlinear Elliptic Equations

The boundary trace problem for positive solutions of $-\Delta u+g(x,u)=0$ is considered for a large class of nonlinearities and three different methods for defining the trace are compared. The boundary trace is usually a generalized Borel measure. The associated Dirichlet problem with boundary data in the set of such Borel measures is studied.