We investigate the stability of radial symmetry for the overdetermined Serrin problem in a planar convex set. More precisely, we prove that, whenever we properly perturb both the boundary conditions and the data, then a convex solution is “close” to a suitable paraboloid and the domain is “close” to a ball with respect to the Hausdorff metric.
A note on the Serrin Problem in the plane / B. Brandolini; C. Nitsch; P. Salani; C. Trombetti. - In: LE MATEMATICHE. - ISSN 0373-3505. - STAMPA. - 63:(2008), pp. 83-92.
A note on the Serrin Problem in the plane
SALANI, PAOLO;
2008
Abstract
We investigate the stability of radial symmetry for the overdetermined Serrin problem in a planar convex set. More precisely, we prove that, whenever we properly perturb both the boundary conditions and the data, then a convex solution is “close” to a suitable paraboloid and the domain is “close” to a ball with respect to the Hausdorff metric.
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