Symmetry and monotonicity of least energy solutions

Details Symmetry and monotonicity of least energy solutions Symmetry and monotonicity of least energy solutions

2008-06-02

arxiv.org/abs/0806.0299v1

Mathematics

Analysis of PDEs

12 pages

Scientific paper

We give a simple proof of the fact that for a large class of quasilinear elliptic equations and systems the solutions that minimize the corresponding energy in the set of all solutions are radially symmetric. We require just continuous nonlinearities and no cooperative conditions for systems. Thus, in particular, our results cannot be obtained by using the moving planes method. In the case of scalar equations, we also prove that any least energy solution has a constant sign and is monotone with respect to the radial variable.

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