Effective energy integral functionals for thin films with bending moment in the Orlicz-Sobolev space setting

Włodzimierz Laskowski; Hôǹg Thái Nguyêñ

Displaying similar documents to “Effective energy integral functionals for thin films with bending moment in the Orlicz-Sobolev space setting”

Effective energy integral functionals for thin films with three dimensional bending moment in the Orlicz-Sobolev space setting

Włodzimierz Laskowski, Hong Thai Nguyen (2016)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we consider an elastic thin film ω ⊂ ℝ² with the bending moment depending also on the third thickness variable. The effective energy functional defined on the Orlicz-Sobolev space over ω is described by Γ-convergence and 3D-2D dimension reduction techniques. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function has the growth prescribed by an Orlicz convex function M. Here M is assumed...

Strongly exposed points in Musielak-Orlicz sequence spaces endowed with Orlicz norm

Zhongrui Shi, Chunyan Liu (2011)

Banach Center Publications

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A criterion for strongly exposed points of the unit ball $B (l_{M})$ in Musielak-Orlicz sequence spaces $l_{M}$ equipped with Orlicz norm is given.

On the density of smooth functions in Sobolev-Orlicz spaces.

Zhikov, V.V. (2004)

Journal of Mathematical Sciences (New York)

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Copies of $l^{1}$ and $c_{o}$ in Musielak-Orlicz sequence spaces

Ghassan Alherk, Henryk Hudzik (1994)

Commentationes Mathematicae Universitatis Carolinae

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Criteria in order that a Musielak-Orlicz sequence space $l^{Φ}$ contains an isomorphic as well as an isomorphically isometric copy of $l^{1}$ are given. Moreover, it is proved that if $Φ = (Φ_{i})$ , where $Φ_{i}$ are defined on a Banach space, $X$ does not satisfy the $δ_{2}^{o}$ -condition, then the Musielak-Orlicz sequence space $l^{Φ} (X)$ of $X$ -valued sequences contains an almost isometric copy of $c_{o}$ . In the case of $X = I R$ it is proved also that if $l^{Φ}$ contains an isomorphic copy of $c_{o}$ , then $Φ$ does not satisfy the $δ_{2}^{o}$ -condition. These results...

Fine behavior of functions whose gradients are in an Orlicz space

Jan Malý, David Swanson, William P. Ziemer (2009)

Studia Mathematica

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For functions whose derivatives belong to an Orlicz space, we develop their "fine" properties as a generalization of the treatment found in [MZ] for Sobolev functions. Of particular importance is Theorem 8.8, which is used in the development in [MSZ] of the coarea formula for such functions.

The importance of being Orlicz

Jürgen Appell (2004)

Banach Center Publications

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On the distribution of random variables corresponding to Musielak-Orlicz norms

David Alonso-Gutiérrez, Sören Christensen, Markus Passenbrunner, Joscha Prochno (2013)

Studia Mathematica

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Given a normalized Orlicz function M we provide an easy formula for a distribution such that, if X is a random variable distributed accordingly and X₁,...,Xₙ are independent copies of X, then $1 / C_{p} {| | x | |}_{M} \leq | | (x_{i} X_{i}) ⁿ_{i = 1} {| |}_{p} \leq C_{p} {| | x | |}_{M}$ , where $C_{p}$ is a positive constant depending only on p. In case p = 2 we need the function t ↦ tM’(t) - M(t) to be 2-concave and as an application immediately obtain an embedding of the corresponding Orlicz spaces into L₁[0,1]. We also provide a general result replacing the $ℓ_{p}$ -norm by an arbitrary...

On the k-convexity of the Besicovitch-Orlicz space of almost periodic functions with the Orlicz norm

Fazia Bedouhene, Mohamed Morsli (2007)

Colloquium Mathematicae

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Boulahia and the present authors introduced the Orlicz norm in the class $B^{ϕ}$ -a.p. of Besicovitch-Orlicz almost periodic functions and gave several formulas for it; they also characterized the reflexivity of this space [Comment. Math. Univ. Carolin. 43 (2002)]. In the present paper, we consider the problem of k-convexity of $B^{ϕ}$ -a.p. with respect to the Orlicz norm; we give necessary and sufficient conditions in terms of strict convexity and reflexivity.

Inductive limit topologies on Orlicz spaces

Marian Nowak (1991)

Commentationes Mathematicae Universitatis Carolinae

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Let $L^{ϕ}$ be an Orlicz space defined by a convex Orlicz function $ϕ$ and let $E^{ϕ}$ be the space of finite elements in $L^{ϕ}$ (= the ideal of all elements of order continuous norm). We show that the usual norm topology $𝒯_{ϕ}$ on $L^{ϕ}$ restricted to $E^{ϕ}$ can be obtained as an inductive limit topology with respect to some family of other Orlicz spaces. As an application we obtain a characterization of continuity of linear operators defined on $E^{ϕ}$ .

On W*UR point and UR point of Orlicz spaces with Orlicz norm.

Ting Fu Wang, Zhong Rui Shi, Quan Di Wang (1993)

Collectanea Mathematica

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For Orlicz spaces with Orlicz norm, a criterion of W*UR point is given, and previous results about UR points and WUR points are amended.

Smooth points of the unit sphere in Musielak-Orlicz function spaces equipped with the Luxemburg norm

Zenon Zbąszyniak (1994)

Commentationes Mathematicae Universitatis Carolinae

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There is given a criterion for an arbitrary element from the unit sphere of Musielak-Orlicz function space equipped with the Luxemburg norm to be a point of smoothness. Next, as a corollary, a criterion of smoothness of these spaces is given.