Symmetry of positive solutions of \(\Delta u + u^ p = 0\) in \(\mathbf R^ n\)
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.
scientific article; zbMATH DE number 790883