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Some new symmetry results for elliptic problems on the sphere and in Euclidean space. (English) Zbl 1008.35002

There are given symmetry results for positive solutions of elliptic problems in \(\mathbb{R}^n\) and on the sphere. The authors consider linear boundary value problems as well as a semilinear problem for the \(p\)-Laplacian operator and the Laplace-Beltrami operator. The techniques utilized are the moving plane method, rearrangement inequalities and stereographic projection.

MSC:

35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35J60 Nonlinear elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35B50 Maximum principles in context of PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
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