Sectional symmetry of solutions of elliptic systems in cylindrical domains

Abstract

In this paper we prove a kind of rotational symmetry for solutions of semilinear elliptic systems in some bounded cylindrical domains. The symmetry theorems obtained hold for low-Morse index solutions whenever the nonlinearities satisfy some convexity assumptions. These results extend and improve those obtained in \cite{DaPaSys, DaGlPa1, Pa, PaWe}.

arXiv commentarXiv admin note: text overlap with arXiv:1209.5581, arXiv:1206.3926