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.
;
2011-01-01
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.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
DCDS(2011).pdf
accesso aperto
Tipologia:
Versione Editoriale
Dimensione
318.36 kB
Formato
Adobe PDF
|
318.36 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
