Results 181 to 190 of about 9,586,445 (221)

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.
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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
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Lower Semicontinuity Properties of Functionals with Free Discontinuities

Archive for Rational Mechanics and Analysis, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Francesco Maddalena, Sergio Solimini
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Lower Semicontinuous Convex Functions

2011
The theory of convex functions is most powerful in the presence of lower semicontinuity. A key property of lower semicontinuous convex functions is the existence of a continuous affine minorant, which we establish in this chapter by projecting onto the epigraph of the function.
Heinz H. Bauschke, Patrick L. Combettes
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L 2-lower semicontinuity of functionals of quadratic type

Annali di Matematica Pura ed Applicata, 1981
A representation formula for the L2-lower semicontinuous envelope of a quadratic integral of Calculus of Variations is given. Some particular cases are explicited in the details.
FUSCO, NICOLA, MOSCARIELLO, GIOCONDA
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Lower Semicontinuous Increasing Functionals

1993
In this chapter we study some properties of the functionals F(x,A) which are lower semicontinuous with respect to x and increasing with respect to A.
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Lower Semicontinuity of Marginal Functions

1984
Criteria for the lower semicontinuity of marginal functions constitute one of the most important topics of optimization.
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Lower semicontinuity of A class of functionals in SBV H

Applied Mathematics-A Journal of Chinese Universities, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Song, Yingqing, Yang, Xiaoping, Long, Fei   +2 more
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Lower semicontinuous convex functions

1989
Our differentiability results for convex functions made heavy and consistent use of continuity, but in both theoretical and applied aspects of convex functions, it is sometimes desirable to weaken this hypothesis. Lower semicontinuity is precisely what is needed.
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Points of Upper and Lower Semicontinuity for Multivalued Functions

Ukrainian Mathematical Journal, 2018
It is known that a multifunction of two variables $F:X\times Y\to Z$, whose $X$ and $Y$ sections are both lower (resp. upper) semicontinuous may be (under usual assumptions on $X$, $Y$, $Z$) non weakly measurable (resp. nonmeasurable), but if the $X$-sections are lsc, the $Y$-sections are usc and the values are compact, it belongs to the upper Borel ...
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