Recently the symmetry of solutions to overdetermined problems has been established for the class of Hessian operators, including the Monge-Ampère operator. In this paper we prove that the radial symmetry of the domain and of the solution to an overdetermined Dirichlet problem for the Monge-Ampère equation is stable under suitable perturbations of the data. © 2008 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.
Brandolini B., Nitsch C., Salani P., Trombetti C. (2009). Stability of radial symmetry for a Monge-Ampère overdetermined problem. ANNALI DI MATEMATICA PURA ED APPLICATA, 188(3), 445-453 [10.1007/s10231-008-0083-4].
Stability of radial symmetry for a Monge-Ampère overdetermined problem
Brandolini B.;
2009-01-01
Abstract
Recently the symmetry of solutions to overdetermined problems has been established for the class of Hessian operators, including the Monge-Ampère operator. In this paper we prove that the radial symmetry of the domain and of the solution to an overdetermined Dirichlet problem for the Monge-Ampère equation is stable under suitable perturbations of the data. © 2008 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.
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