On the strong solvability of a unilateral boundary value problem for nonlinear discontinuous operators in the plane (Q2771631)

A uniqueness and existence theorem in the Sobolev space is proved for a unilateral boundary value problem for a class of nonlinear discontinuous operators in the plane. The operator is assumed to satisfy a suitable ellipticity condition, which allows us to apply nearness theory of mappings. The estimate NEWLINE\[NEWLINE\int_\Omega \sum^2_{i,j=1} \left({\partial^2 u\over \partial x_i\partial x_j} \right)^2 \,dx\leq\int_\Omega |\Delta u|^2 \,dx,NEWLINE\]NEWLINE NEWLINE\[NEWLINEu\in W^{2,2}(\Omega): u\geq 0,\;{\partial u\over\partial n}\geq 0,\;u\cdot{\partial u\over\partial n}= 0\text{ on }\partial\OmegaNEWLINE\]NEWLINE having interest in itself, plays a fundamental role.NEWLINENEWLINEFor the entire collection see [Zbl 0992.49001].