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Analogue of Gidas-Ni-Nirenberg result in hyperbolic space and sphere
Kumaresan, S.
Prajapat, Jyotshana
1998
Abstract
Let $u\epsilon C^{2}\left(\overline{\Omega}\right)$be a positive
solution of the differential equation $\Delta u+f\left(u\right)=0$
in $\Omega$ with boundary condition u=0 on $\partial\Omega$ where
f is a C$^{1}$ function and $\Omega$ is a geodesic ball in the hyperbolic
space $\mathbf{H}^{\mathbf{n}}$ $\left(\textrm{respectively}\:\textrm{sphere}\:\mathbf{S^{\mathbf{n}}}\right)$.
Further in case of sphere we assume that $\overline{\Omega}$ is contained
in a hemisphere. Then we prove that u is radially symmetric.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
30 (1998)
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
S. Kumaresan and J. Prajapat, "Analogue of Gidas-Ni-Nirenberg result in hyperbolic space and sphere", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 30 (1998), pp. 107-112.
Languages
en
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