JournalsrlmVol. 24, No. 1pp. 39–81

Mixed type, nonlinear systems in polygonal domains

  • Vsevolod A. Solonnikov

    Russian Acadademy of Sciences, St. Petersburg, Russian Federation
  • Maria Agostina Vivaldi

    Università di Roma La Sapienza, Italy
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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 ΩR2\Omega\subset \R^2 whose boundary is smooth everywhere except a single angular point x=0x=0 with the aperture of the angle θ>π\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.

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. 39–81

DOI 10.4171/RLM/644