In this note we prove that, if Ω is a smooth, strictly convex, open set in R n (n ≥ 2) with given measure, the L 1 norm of the convex solution to the Dirichlet problem detD 2u = 1 in , u = 0 on δΩ, is minimum whenever is an ellipsoid.

Brandolini B., Nitsch C., & Trombetti C. (2011). Shape optimization for monge-ampére equations via domain derivative. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 4(4), 825-831 [10.3934/dcdss.2011.4.825].

Shape optimization for monge-ampére equations via domain derivative

Brandolini B.
;
2011

Abstract

In this note we prove that, if Ω is a smooth, strictly convex, open set in R n (n ≥ 2) with given measure, the L 1 norm of the convex solution to the Dirichlet problem detD 2u = 1 in , u = 0 on δΩ, is minimum whenever is an ellipsoid.
Settore MAT/05 - Analisi Matematica
Brandolini B., Nitsch C., & Trombetti C. (2011). Shape optimization for monge-ampére equations via domain derivative. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 4(4), 825-831 [10.3934/dcdss.2011.4.825].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/494001
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