6533b852fe1ef96bd12aa453
RESEARCH PRODUCT
On the stability of the Serrin problem
Barbara BrandoliniCarlo NitschCristina TrombettiPaolo Salanisubject
Applied MathematicsMathematical analysisSymmetry in biologyDisjoint setsUnitary stateStability (probability)Domain (mathematical analysis)Overdetermined systemSettore MAT/05 - Analisi MatematicaOverdetermined problemOverdetermined problemsStabilityAnalysisMathematicsdescription
We investigate stability issues concerning the radial symmetry of solutions to Serrin's overdetermined problems. In particular, we show that, if $u$ is a solution to $\Delta u=n$ in a smooth domain $\Omega \subset \rn$, $u=0$ on $\partial\Omega$ and $|Du|$ is close to 1 on $\partial\Omega$, then $\Omega$ is close to the union of a certain number of disjoint unitary balls.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-09-01 |