In ℝ m ×ℝ n-m, endowed with coordinates x=(x′,x″), we consider bounded solutions of the PDE Δ u(x)=f(u(x))χ(x'). We prove a geometric inequality, from which a symmetry result follows.
Elliptic PDEs with fibered nonlinearities / O. Savin, E. Valdinoci. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 19:2(2009), pp. 420-432.
Elliptic PDEs with fibered nonlinearities
E. ValdinociPrimo
2009
Abstract
In ℝ m ×ℝ n-m, endowed with coordinates x=(x′,x″), we consider bounded solutions of the PDE Δ u(x)=f(u(x))χ(x'). We prove a geometric inequality, from which a symmetry result follows.
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