Recently the symmetry of solutions to overdetermined problems has been established for the class of Hessian operators, including theMonge-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.
Stability of radial symmetry for a Monge-Ampère overdetermined problem / B. Brandolini; C. Nitsch; P. Salani; C. Trombetti. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 188 n.3:(2009), pp. 445-453. [10.1007/s10231-008-0083-4]
Stability of radial symmetry for a Monge-Ampère overdetermined problem
SALANI, PAOLO;
2009
Abstract
Recently the symmetry of solutions to overdetermined problems has been established for the class of Hessian operators, including theMonge-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.
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