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Symmetry of positive solutions of \(\Delta u + u^ p = 0\) in \(\mathbf R^ n\). (English) Zbl 0844.35028

The Lane-Emden equation \(\Delta u+ u^p= 0\) is considered in \(\mathbb{R}^n\), \(n> 2\). Conditions are established for a nontrivial nonnegative solution of this equation to be radially symmetric. Hölder type and Lipschitz type estimates and the Alexandroff-Serrin moving plane method are applied.

MSC:

35J60 Nonlinear elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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