Symmetry results for perturbed problems and related questions

Massimo Grossi, Filomena Pacella, S. L. Yadava

DOI: http://dx.doi.org/10.12775/TMNA.2003.013

Abstract


In this paper we prove a symmetry result for positive solutions of the Dirichlet problem
$$
\cases
-\Delta u=f(u) & \hbox{in }D,\\
u=0 & \hbox{on }\partial D,
\endcases
\tag{0.1}
$$
when $f$ satisfies suitable assumptions and $D$ is a small symmetric perturbation of a domain $\Omega$
for which the Gidas-Ni-Nirenberg symmetry theorem applies.
We consider both the case when $f$ has subcritical growth and $f(s)=s^{(N+2)/(N-2)}+\lambda s$,
$N\ge3$, $\lambda$ suitable positive constant.

Keywords


Elliptic equations; symmetry of solutions

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