## Asymptotic symmetry for a class of quasi-linear parabolic problems.(English)Zbl 1253.35009

Summary: We study the symmetry properties of the weak positive solutions to a class of quasillinear elliptic problems having a variational structure. On this basis, the asymptotic behaviour of global solutions of the corresponding parabolic equations is also investigated. In particular, if the domain is a ball, the elements of the $$\omega$$ limit set are nonnegative radially symmetric solutions of the stationary problem.

### MSC:

 35B06 Symmetries, invariants, etc. in context of PDEs 35B40 Asymptotic behavior of solutions to PDEs 35A30 Geometric theory, characteristics, transformations in context of PDEs 35B09 Positive solutions to PDEs 35J20 Variational methods for second-order elliptic equations 35K20 Initial-boundary value problems for second-order parabolic equations 35J25 Boundary value problems for second-order elliptic equations 35J92 Quasilinear elliptic equations with $$p$$-Laplacian 35K92 Quasilinear parabolic equations with $$p$$-Laplacian
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