Results 91 to 100 of about 9,586,445 (221)
Weak Lower Semicontinuity of a Functional with Any Order
Journal of Mathematical Analysis and Applications, 1998 The author extends the necessary and sufficient quasiconvexity conditions for the sequential weak lower semicontinuity of a functional of the type \[ u\in W^{k,p}(\Omega; \mathbb{R}^m)\mapsto \int_\Omega f(x,u,Du, D^2u,\dots, D^ku)dx,\tag{1} \] where \(\Omega\) is a bounded open subset of \(\mathbb{R}^n\), \(p\in ]1,+\infty]\), and \(m\geq 1\), to the ...
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Existence of solutions for nonconvex functional differential inclusions
Electronic Journal of Differential Equations, 2004 We prove the existence of solutions for the functional differential inclusion $x'in F(T(t)x)$, where $F$ is upper semi-continuous, compact-valued multifunction such that $F(T(t)x)subset partial V(x(t))$ on $[0,T]$, $V$ is a proper convex and lower ...
Vasile Lupulescu
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Lower semicontinuous solutions to Hamilton-Jacobi-Bellman equations
, 1993 The value function of Mayer’s problem arising in optimal control is investigated, and lower semicontinuous solutions of the associated Hamilton–Jacobi–Bellman equation are defined in three (equivalent) ways. Under quite weak assumptions about the control
Frankowska, Halina
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On the lower semicontinuous quasiconvex envelope for unbounded integrands (I) [PDF]
, 2009 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 $\subset \mathbb{R}^{nm}$ instead of the whole ...
Marcus Wagner, Wagner, Marcus
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A convex extension of lower semicontinuous functions defined on normal Hausdorff space
, 2017 We prove that, any problem of minimization of proper lower semicontinuous function defined on a normal Hausdorff space, is canonically equivalent to a problem of minimization of a proper weak * lower semicontinuous convex function defined on a weak ...
Bachir, Mohammed
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Existence theorems for differential inclusions with nonconvex right hand side
International Journal of Mathematics and Mathematical Sciences, 1986 In this paper we prove some new existence theorems for differential inclusions with a nonconvex right hand side, which is lower semicontinuous or continuous in the state variable, measurable in the time variable and takes values in a finite or infinite ...
Nikolaos S. Papageorgiou
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Two -person zero-sum stochastic games with semicontinuous payoff [PDF]
Considérons un jeu stochastique à deux joueurs et à somme-nulle avec un espace d'état Borélien S, des espaces d'actions métriques et compacts A, B et une probabilité de transition q telle que l'intégrale sous q de toute fonction mesurable et bornée ...
William Sudderth +2 more
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Extensions of semicontinuous and quasi-continuous functions from dense subspaces
, 2021 In this paper we give a sufficient condition for existence of an extension of a lower (upper) semicontinuous function 0 defined on a given dense subset of a topological space X to a lower (upper) semicontinuous function : X → ℝ.
Kosman, Jolanta
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Gateaux Differentiability of Convex Functions and Weak Dentable Set in Nonseparable Banach Spaces
Journal of Function Spaces, 2019 In this paper, we prove that if C⁎⁎ is a ε-separable bounded subset of X⁎⁎, then every convex function g≤σC is Ga^teaux differentiable at a dense Gδ subset G of X⁎ if and only if every subset of ∂σC(0)∩X is weakly dentable.
Shaoqiang Shang, Yunan Cui
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On the Sums of Lower Semicontinuous Strong Świątkowski Functions
Real Analysis Exchange, 2014 The purpose of this article is to give a solution to a problem raised by A. Maliszewski in \(\left[5\right]\) by showing that any lower semicontinuous function can be represented as a sum of two lower semicontinuous strong \'{S}wi\k{a}tkowski functions.
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