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RESEARCH PRODUCT

New isoperimetric estimates for solutions to Monge - Ampère equations

Carlo NitschBarbara BrandoliniCristina Trombetti

subject

Dirichlet problemMonge-Ampère operatoreigenvalue.Mathematics::Complex VariablesApplied MathematicsMathematical analysisMathematics::Analysis of PDEsMonge–Ampère equationMonge-Ampère equationMathematics::Spectral TheoryMeasure (mathematics)Operator (computer programming)Settore MAT/05 - Analisi MatematicaAffine isoperimetric inequaltieRayleigh–Faber–Krahn inequalityAffine isoperimetric inequalitiesIsoperimetric inequalityLaplace operatorMathematical PhysicsAnalysisEigenvalues and eigenvectorsMathematics

description

Abstract We prove some sharp estimates for solutions to Dirichlet problems relative to Monge–Ampere equations. Among them we show that the eigenvalue of the Dirichlet problem, when computed on convex domains with fixed measure, is maximal on ellipsoids. This result falls in the class of affine isoperimetric inequalities and shows that the eigenvalue of the Monge–Ampere operator behaves just the contrary of the first eigenvalue of the Laplace operator.

yearjournalcountryeditionlanguage
2009-01-01
10.1016/j.anihpc.2008.09.005http://hdl.handle.net/11588/301556