Displaying similar documents to “Jensen-type geometric shapes”

Optimal convex shapes for concave functionals

Dorin Bucur, Ilaria Fragalà, Jimmy Lamboley (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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Motivated by a long-standing conjecture of Pólya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their ...

Optimal convex shapes for concave functionals

Dorin Bucur, Ilaria Fragalà, Jimmy Lamboley (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

Motivated by a long-standing conjecture of Pólya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their ...

Classical solids.

Farran, H.R., d'Azevedo Breda, A.M., Robertson, S.A. (1995)

Beiträge zur Algebra und Geometrie

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Optimal convex shapes for concave functionals

Dorin Bucur, Ilaria Fragalà, Jimmy Lamboley (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

Motivated by a long-standing conjecture of Pólya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and we provide several counterexamples to the Blaschke-concavity of variational functionals, including capacity. We then introduce a new algebraic structure on convex bodies, which allows to obtain global concavity and indecomposability results, and we discuss their application to isoperimetric-like inequalities....