Displaying similar documents to “Isoperimetric problems for a nonlocal perimeter of Minkowski type”

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 application to isoperimetric-like inequalities....

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 ...

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 ...

On unit balls and isoperimetrices in normed spaces

Horst Martini, Zokhrab Mustafaev (2012)

Colloquium Mathematicae

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The purpose of this paper is to continue the investigations on the homothety of unit balls and isoperimetrices in higher-dimensional Minkowski spaces for the Holmes-Thompson measure and the Busemann measure. Moreover, we show a strong relation between affine isoperimetric inequalities and Minkowski geometry by proving some new related inequalities.

On the analysis of boundary value problems in nonsmooth domains

Gilles Frémiot, Werner Horn, Antoine Laurain, Murali Rao, Jan Sokołowski

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Problems involving cracks are of particular importance in structural mechanics, and gave rise to many interesting mathematical techniques to treat them. The difficulties stem from the singularities of domains, which yield lower regularity of solutions. Of particular interest are techniques which allow us to identify cracks and defects from the mechanical properties. Long before advent of mathematical modeling in structural mechanics, defects were identified by the fact that they changed...

A quantitative version of the isoperimetric inequality : the anisotropic case

Luca Esposito, Nicola Fusco, Cristina Trombetti (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We state and prove a stability result for the anisotropic version of the isoperimetric inequality. Namely if E is a set with small anisotropic isoperimetric deficit, then E is “close” to the Wulff shape set.

A Survey on Vector Variational Inequalities

F. Giannessi, G. Matroeni, X. Q. Yang (2009)

Bollettino dell'Unione Matematica Italiana

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The paper consists in a brief overview on Vector Variational Inequalities (VVI). The connections between VVI and Vector Optimization Problems (VOP) are considered. This leads to point out that necessary optimality conditions for a VOP can be formulated by means of a VVI when the objective function is Gâteaux differentiable and the feasible set is convex. In particular, the existence of solutions and gap functions associated with VVI are analysed. Gap functions provide an equivalent formulation...

Shape optimization for dynamic contact problems

Andrzej Myśliński (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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The paper deals with shape optimization of dynamic contact problem with Coulomb friction for viscoelastic bodies. The mass nonpenetrability condition is formulated in velocities. The friction coefficient is assumed to be bounded. Using material derivative method as well as the results concerning the regularity of solution to dynamic variational inequality the directional derivative of the cost functional is calculated and the necessary optimality condition is formulated.