6533b852fe1ef96bd12aade0

RESEARCH PRODUCT

Stability of radial symmetry for a Monge-Ampère overdetermined problem

Carlo NitschPaolo SalaniBarbara BrandoliniCristina Trombetti

subject

Hessian matrixDirichlet problemoverdetermined problemMathematics::Complex VariablesApplied MathematicsMathematical analysisMathematics::Analysis of PDEsSymmetry in biologyMonge–Ampère equationMonge-Ampère equationComputer Science::Numerical AnalysisDomain (mathematical analysis)Symmetry (physics)Overdetermined systemsymbols.namesakeOperator (computer programming)Settore MAT/05 - Analisi MatematicasymbolsOverdetermined problemsStabilityIsoperimetric inequalityMathematics

description

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.

yearjournalcountryeditionlanguage
2008-09-17
10.1007/s10231-008-0083-4http://hdl.handle.net/10447/494028