Results 1 to 10 of about 15 (13)

Some new results on a Lavrentieff phenomenon for problems of homogenization with constraints on the gradient

Le Matematiche, 1999
In this paper we analyze, in the context of a Lavrentieff phenomenon, the process of homogenization for Dirichlet problems.
C. D'Apice, T. Durante, A. Gaudiello
doaj   +6 more sources

On the existence of weak optimal BV-controls in coefficients for linear elliptic problems

Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ, 2009
In this paper we study the optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. We adopt a weight coefficient in the main part of elliptic operator as control in BV(Ω).
I. G. Balanenko, P. I. Kogut
doaj   +1 more source

H-Optimal Control in Coefficients for Dirichlet Parabolic Problems

Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Modelûvannâ, 2010
In the paper the Dirichlet optimal control problem associated with a linear parabolic equation the coefficients of which we take as controls in L1(Ω) has been studied. Since equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness
I. G. Balanenko, P. I. Kogut
doaj   +1 more source

Inward pointing trajectories, normality of the maximum principle and the non occurrence of the Lavrentieff phenomenon in optimal control under state constraints

, 2013
Summary: It is well known that every strong local minimizer of the Bolza problem under state constraints satisfies a constrained maximum principle. In the absence of constraints qualifications the maximum principle may be abnormal, that is, not involving the cost functions.
Frankowska, Hélène, Tonon, Daniela
openaire   +3 more sources

The Lavrentieff phenomenon And Different processes of Homogenization

Communications in Partial Differential Equations, 1992
(1992). The Lavrentieff phenomenon And Different processes of Homogenization. Communications in Partial Differential Equations: Vol. 17, No. 9-10, pp. 1503-1538.
Esposito Antonio Corbo, null Riccardo De Arcagelis   +1 more
openaire   +3 more sources

Complete representation of some functionals showing the Lavrentieff phenomenon

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2001
The functional F(u) = ∫Bf(x, Du) is considered, where B is the unit ball in R2, u varies in the set of the locally Lipschitz functions on R2 and f belongs to a family containing, as model case, the following integrand: The computation of the relaxed functional F̄ is provided yielding an explicit representation formula.This formula nevertheless is not ...
A. CORBO ESPOSITO, DURANTE, Tiziana
openaire   +2 more sources

On the relaxation and the Lavrentieff phenomenon for variational integrals with pointwise measurable gradient constraints

Calculus of Variations and Partial Differential Equations, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
DE ARCANGELIS R., MONSURRO', SARA, ZAPPALE, ELVIRA   +2 more
openaire   +5 more sources

The Lavrentieff phenomenon for quadratic functionals

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1995
The paper provides an example of an integral functional in more than two dimensions, with a symmetric and positively defined quadratic integrandq, exhibiting the Lavrentieff phenomenon on a ballBand on a linear boundary datumu0, i.e. for whichThe example is also utilised to discuss nonidentity between some relaxation procedures for a quadratic integral
openaire   +1 more source

Lavrentieff phenomenon and non standard growth conditions

2001
In the paper the functional \[ F(u)= \int_B f(x,Du) dx \] is considered, where \(B\) is the unit ball in \(\mathbb{R}^n\) and \(u\) varies among Lipschitz functions. The integrand \(f\) belongs to a family containing, as a model case, the function \[ f(x,z)= {|z\cdot x|\over|x|^n}+|z|^p\quad\text{with }1< p< n.
CARDONE G., D'APICE C., DE MAIO, UMBERTO
openaire   +3 more sources

A Lavrentieff phenomenon for problems of homogenization with constraints on the gradient

1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Corbo Esposito, Serra Cassano, Francesco   +1 more
openaire   +3 more sources