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Symmetry of positive solutions of a quasilinear elliptic equation via isoperimetric inequalities. (English) Zbl 0833.35040

It is proved that positive solutions of nonlinear equations involving the \(N\)-Laplacian in a ball in \(\mathbb{R}^N\) with Dirichlet boundary conditions are radial and radially decreasing provided that the nonlinearity is a continuous function \(f(t)\) (satisfying suitable growth conditions) which is strictly positive for \(t> 0\). The method generalizes that of Lions for the Laplacian in two dimensions. The method of the present paper can also be extended to an analogous mixed boundary value problem in a convex cone.

MSC:

35J60 Nonlinear elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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References:

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