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.
On the stability of the Serrin problem / Brandolini, Barbara; Nitsch, Carlo; P., Salani; Trombetti, Cristina. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 245:(2008), pp. 1566-1583. [10.1016/j.jde.2008.06.010]
On the stability of the Serrin problem
BRANDOLINI, BARBARA;NITSCH, CARLO;TROMBETTI, CRISTINA
2008
Abstract
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.File in questo prodotto:
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