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 of 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.
Mixed type, nonlinear systems in polygonal domains / Vsevolod, Solonnikov; Vivaldi, Maria Agostina. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - STAMPA. - 24:1(2013), pp. 39-81. [10.4171/rlm/644]
Mixed type, nonlinear systems in polygonal domains
VIVALDI, Maria Agostina
2013
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 of 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.