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Some connections between symmetry results for semilinear PDE in real and hyperbolic spaces |
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| Authors: | Luí s Almeida,Yuxin Ge |
| Affiliation: | a Laboratoire J.A. Dieudonné, CNRS UMR 6621, Université de Nice, Sophia-Antipolis, Parc Valrose, 06108 Nice Cédex 02, France b Département de Mathématiques, Faculté de Sciences et Technologie, Université Paris XII, Val de Marne, 61, avenue du Général de Gaulle, 94010 Créteil cédex, France c Dipartimento di Matematica, Universitá di Verona, Italy |
| Abstract: | Taking advantage of the “invariance” under conformal transformations of certain elliptic operators and combining it with symmetry results obtained by moving totally geodesic hypersurfaces in Hn, we are able to prove the symmetry of positive solutions of −Δu=f(r,u), in balls in Rn, for a class of nonlinearities that do not satisfy the classical hypothesis of f being decreasing in r. |
| Keywords: | Symmetry Moving planes method Hyperbolic space Totally geodesic hypersurfaces Positive solutions of elliptic PDE |
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