Mixed type, nonlinear systems in polygonal domains

Abstract

We prove existence, uniqueness results and coercive estimates in the weighted Sobolev spaces for a linear problem of mixed type in a bounded domain $\Omega \subset {\mathbb{R}}^2$ whose boundary is smooth everywhere except a single angular point $x=0$ with the aperture of the angle $\theta >\pi$. In addition, we establish a stability result for a non-linear system of mixed type. The results of the paper and the proofs extend to the case of polygonal domains.