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- W1983161195 abstract "We prove some symmetry theorems for positive solutions of elliptic equations in some noncompact manifolds, which generalize and extend symmetry results known in the case of the euclidean space Rn. The (variational) technique that we use relies on Sobolev inequalities available for manifolds together with the well known method of moving planes. In the particular case of the standard n-dimensional hyperbolic space Hn we get the radial symmetry of positive solutions of the equation −ΔHnu=f(u) in Hn, which tend to zero at infinity (or belong to the Sobolev space H1(Hn) in some cases), under different hypotheses on the relationship between the behavior of the nonlinearity f in a neighborhood of zero and the summability properties of the solution. One of the main features of this work is to single out and study the connection between the geometric properties of the manifold considered and the growth conditions on the nonlinearity in order to have our symmetry results." @default.
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- W1983161195 date "2002-01-01" @default.
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- W1983161195 title "A few symmetry results for nonlinear elliptic PDE on noncompact manifolds" @default.
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- W1983161195 doi "https://doi.org/10.1016/s0294-1449(01)00091-9" @default.
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