Results 141 to 150 of about 336 (182)

On lower semicontinuity in BH and 2-quasiconvexification

Calculus of Variations and Partial Differential Equations, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fonseca, Irene, Leoni, Giovanni, Paroni, Roberto   +2 more
openaire   +4 more sources

Counterexample to lower semicontinuity in Calculus of Variations

Mathematische Zeitschrift, 2001
In the present paper the authors give an example of a functional \[ F(u)=\int _0^1 f(u(t),u^\prime (t))dt \] defined on the Sobolev space \(W^{1,1}((0,1),\mathbb{R}^2)\) for which the \(L^1\)-lower semicontinuity doesn't hold. This example shows that no reasonable extension of the functional \(F\) to the space BV has a minimizer.
Černý, Robert, Malý, Jan
openaire   +1 more source

On Lower Semicontinuity of Integral Functionals. II

SIAM Journal on Control and Optimization, 1977
A necessary and sufficient condition for the integral functional $I(x( \cdot ),y( \cdot )) = \smallint _G f(t,x(t),y(t))d\mu $ to be sequentially lower semicontinuous with respect to some kinds of strong convergence of $x( \cdot )$components and weak convergence of $y( \cdot )$-components is proved.
openaire   +3 more sources

Lower Semicontinuity of Multivalued Linearization Mappings

SIAM Journal on Control, 1973
Many results in mathematical programming require lower semicontinuity of the multi-valued function obtained from a constraint set by replacing the functions defining the set by their linearizations about a point. In this paper we give a simple sufficient condition, involving the gradients of the active linearized constraints, for this property to hold.
Robinson, Stephen M., Meyer, Robert R.
openaire   +2 more sources

On error bounds for lower semicontinuous functions

Mathematical Programming, 2002
This paper refines earlier results from [\textit{K. F. Ng, X. Y. Zheng}, SIAM J. Optim. 12, No. 1, 1--17 (2001; Zbl 1040.90041)] on error bounds for lower semicontinuous functions \(f:X\rightarrow {\mathbb R}\) defined on a metric space \(X.\) In particular, the authors consider error bounds with exponent \(\beta >0,\) in which the distance from \(x\in
Zili Wu, Jane J. Ye
openaire   +2 more sources

Lower Semicontinuity in SBV for Integrals with Variable Growth

SIAM Journal on Mathematical Analysis, 2010
We prove a lower semicontinuity result for free discontinuity energies with a quasiconvex volume term having nonstandard growth and a surface term.
V. DE CICCO, LEONE, CHIARA, VERDE, ANNA
openaire   +3 more sources

Remarks on lower semicontinuity and lower closure

Journal of Optimization Theory and Applications, 1976
In the context of a recent geometric condition of Cesari, used in the reduction of seminormality requirements in lower closure theorems, this paper shows that the existence of a strongly convergent selection from the sequence of orientor fields, under Kuratowski property (K), is adequate to guarantee lower closure theorems.
openaire   +1 more source

Lower Semicontinuity of a Non-Hyperbolic Attractor

Journal of the London Mathematical Society, 1995
The unstable invariant set near a non-hyperbolic stationary point of an abstract parabolic equation is studied. Lower semicontinuity of the attractor for the Chafee-Infante problem in the case of the non-hyperbolic zero stationary solution is proved.
openaire   +2 more sources

The Failure of Lower Semicontinuity For The Linear Dilatation

Bulletin of the London Mathematical Society, 1998
The following theorem is proved. Theorem. For each dimension \(n \geq 3\) and dilatation \(K >1,\) there exists a sequence \((f_j)\) of \(K\)-quasiconformal mappings \(f_j: \mathbb{R}^n \to \mathbb{R}^n\) converging uniformly to a linear map \(f: \mathbb{R}^n \to \mathbb{R}^n\) whose dilatation is greater than \(K .\) The dilatation here refers to the ...
openaire   +2 more sources

On the Cone of Bounded Lower Semicontinuous Functions

Mathematical Notes, 2005
For a topological space \(X\), let \(BC(X)\) be the Banach space of all bounded, real-valued continuous functions on \(X\), endowed with the ordinary addition and multiplication and the partial order: \[ f_1\geq f_2\quad\text{iff }f_1(x)\geq f_2(x)\quad\text{for all }x\in X, \] and the sup-norm \(\| f\|= \sup\{|f(x)|: x\in X\}\). \(BC(X)_\sim\) denotes
openaire   +1 more source