Subsolutions of elliptic equations in L-1

We study subsolutions for semilinear elliptic boundary value problems in L- 1. We consider as well nonlinear as linear boundary conditions. The nonline ar functions may be multivated. We characterize in terms of p.d.e. the subs olutions defined by a nonlinear functional analysis argument. Applications are given to obtain existence results for semilinear elliptic boundary valu e problems and comparison and estimates for nonlinear parabolic boundary va lue problems.