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Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains. (English) Zbl 0741.35014
The author introduces a new approach for studying the monotonicity and symmetry in one direction of positive \(C^ 2\) solutions of the following fully nonlinear elliptic equation \(F(x,u,u_ i,u_{ij})=0\) in \(\mathbb{R}^ n\), \(| u(x)| +| Du| +| D^ 2u|\to 0\) uniformly as \(| x| \to \infty\).
Reviewer: V.Mustonen (Oulu)

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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