On a nonlinear elliptic boundary value problem
On a nonlinear elliptic boundary value problem
Consider a bounded domain $G \subset {R^N}(N \geq 1)$ with smooth boundary $\Gamma$. Let $L$ be a uniformly elliptic linear differential operator. Let $\gamma$ and $\beta$ be two maximal monotone mappings in $R$. We prove that, when $\gamma$ satisfies a certain growth condition, given $f \in {L^2}(G)$ there is $u …