We study positive solutions $u$ to $\Delta u+f(u)=0$ in $\Omega$, $u=0$ on $\partial\Omega$, and we address the following question: if $\Omega$ is a small perturbation of a ball, is $u$ a small perturbation of a radially symmetric function? We prove two theorems which give an affirmative answer under different assumptions on the non-linearity $f$ and on the topologies in which perturbations are considered.
An approximate Gidas-Ni-Nirenberg theorem
ROSSET, EDI
1994-01-01
Abstract
We study positive solutions $u$ to $\Delta u+f(u)=0$ in $\Omega$, $u=0$ on $\partial\Omega$, and we address the following question: if $\Omega$ is a small perturbation of a ball, is $u$ a small perturbation of a radially symmetric function? We prove two theorems which give an affirmative answer under different assumptions on the non-linearity $f$ and on the topologies in which perturbations are considered.File in questo prodotto:
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