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 [ 6 , 9 , 16 , 18 ].