Displaying 341 – 360 of 562

Showing per page

On the lower semicontinuity of supremal functionals

Michele Gori, Francesco Maggi (2003)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study the lower semicontinuity problem for a supremal functional of the form F ( u , Ω ) = ess sup x Ω f ( x , u ( x ) , D u ( x ) ) with respect to the strong convergence in L ( Ω ) , furnishing a comparison with the analogous theory developed by Serrin for integrals. A sort of Mazur’s lemma for gradients of uniformly converging sequences is proved.

On the Lower Semicontinuity of Supremal Functionals

Michele Gori, Francesco Maggi (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study the lower semicontinuity problem for a supremal functional of the form F ( u , Ω ) = ess sup x Ω f ( x , u ( x ) , D u ( x ) ) with respect to the strong convergence in L∞(Ω), furnishing a comparison with the analogous theory developed by Serrin for integrals. A sort of Mazur's lemma for gradients of uniformly converging sequences is proved.

On the lower semicontinuous quasiconvex envelope for unbounded integrands (I)

Marcus Wagner (2009)

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by the study of multidimensional control problems of Dieudonné-Rashevsky type, we raise the question how to understand to notion of quasiconvexity for a continuous function f with a convex body K n m instead of the whole space n m as the range of definition. In the present paper, we trace the consequences of an infinite extension of f outside K, and thus study quasiconvex functions which are allowed to take the value +∞. As an appropriate envelope, we introduce and investigate the lower semicontinuous...

On the numerical modeling of deformations of pressurized martensitic thin films

Pavel Bělík, Timothy Brule, Mitchell Luskin (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We propose, analyze, and compare several numerical methods for the computation of the deformation of a pressurized martensitic thin film. Numerical results have been obtained for the hysteresis of the deformation as the film transforms reversibly from austenite to martensite.

On the Numerical Modeling of Deformations of Pressurized Martensitic Thin Films

Pavel Bělík, Timothy Brule, Mitchell Luskin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose, analyze, and compare several numerical methods for the computation of the deformation of a pressurized martensitic thin film. Numerical results have been obtained for the hysteresis of the deformation as the film transforms reversibly from austenite to martensite.

On the quasiconvex exposed points

Kewei Zhang (2001)

ESAIM: Control, Optimisation and Calculus of Variations

The notion of quasiconvex exposed points is introduced for compact sets of matrices, motivated from the variational approach to material microstructures. We apply the notion to give geometric descriptions of the quasiconvex extreme points for a compact set. A weak version of Straszewicz type density theorem in convex analysis is established for quasiconvex extreme points. Some examples are examined by using known explicit quasiconvex functions.

On the quasiconvex exposed points

Kewei Zhang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The notion of quasiconvex exposed points is introduced for compact sets of matrices, motivated from the variational approach to material microstructures. We apply the notion to give geometric descriptions of the quasiconvex extreme points for a compact set. A weak version of Straszewicz type density theorem in convex analysis is established for quasiconvex extreme points. Some examples are examined by using known explicit quasiconvex functions.

On the Representation of Effective Energy Densities

Christopher J. Larsen (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the question raised in [1] of whether relaxed energy densities involving both bulk and surface energies can be written as a sum of two functions, one depending on the net gradient of admissible functions, and the other on net singular part. We show that, in general, they cannot. In particular, if the bulk density is quasiconvex but not convex, there exists a convex and homogeneous of degree 1 function of the jump such that there is no such representation.

On the structure of symmetric 2 x 2 gradients.

Pablo Pedregal (2003)

RACSAM

A way of geometrically representing symmetric 2 × 2-gradients is proposed, and a general theorem characterizing sets of gradients is proved. We believe this perspective may help in understanding the structure of gradients and visualizing it. Several non-trivial examples are discussed.

On the unique extension problem for functionals of the calculus of variations

Luciano Carbone, Riccardo De Arcangelis (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

By drawing inspiration from the treatment of the non parametric area problem, an abstract functional is considered, defined for every open set in a given class of open subsets of R n and every function in C R n , and verifying suitable assumptions of measure theoretic type, of invariance, convexity, and lower semicontinuity. The problem is discussed of the possibility of extending it, and of the uniqueness of such extension, to a functional verifying analogous properties, but defined in wider families...

On the well-posedness of some optimal control problems

Augusto Visintin (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si considerano problemi di controllo ottimale con una dipendenza non lineare tra il controllo e lo stato. Si mostra come in certi casi la continuità di tale dipendenza, quindi la buona posizione nel senso di Tychonov, è connessa alla forma del funzionale costo. In particolare si esamina un problema di Stefan a due fasi con controllo distribuito nel termine di sorgente.

Currently displaying 341 – 360 of 562