We prove existence, uniqueness results and coercive estimates in the weighted Sobolev spaces for a linear problem of mixed type in a bounded domain whose boundary is smooth everywhere except a single angular point with the aperture of the angle . 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.
Cite this article
Vsevolod A. Solonnikov, Maria Agostina Vivaldi, Mixed type, nonlinear systems in polygonal domains. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 24 (2013), no. 1, pp. 39–81DOI 10.4171/RLM/644