Symmetry results for nonvariational quasi-linear elliptic systems. (English) Zbl 1227.35036

Montoro, Luigi; Sciunzi, Berardino; Squassina, Marco

Adv. Nonlinear Stud. 10, No. 4, 939-955 (2010).

Summary: By virtue of a weak comparison principle in small domains we prove axial symmetry in convex and symmetric smooth bounded domains as well as radial symmetry in balls for regular solutions of a class of quasi-linear elliptic systems in non-variational form. Moreover, in the two-dimensional case, we study the system when set in a half-space.

MSC:

35B06	Symmetries, invariants, etc. in context of PDEs
35J57	Boundary value problems for second-order elliptic systems
35J62	Quasilinear elliptic equations

Keywords:

axial symmetry; radial symmetry; weak comparison principle; convex and symmetric domains; non-variational form