We prove some sharp estimates for solutions to Dirichlet problems relative to Monge-Ampère 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-Ampère operator behaves just the contrary of the first eigenvalue of the Laplace operator.

Brandolini B., Nitsch C., & Trombetti C. (2009). New isoperimetric estimates for solutions to Monge-Ampère equations. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 26(4), 1265-1275 [10.1016/j.anihpc.2008.09.005].

New isoperimetric estimates for solutions to Monge-Ampère equations

Brandolini B.;
2009

Abstract

We prove some sharp estimates for solutions to Dirichlet problems relative to Monge-Ampère 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-Ampère operator behaves just the contrary of the first eigenvalue of the Laplace operator.
Settore MAT/05 - Analisi Matematica
Brandolini B., Nitsch C., & Trombetti C. (2009). New isoperimetric estimates for solutions to Monge-Ampère equations. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 26(4), 1265-1275 [10.1016/j.anihpc.2008.09.005].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/494046
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