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

Włodzimierz Laskowski, Hôǹg Thái Nguyêñ (2014)

Banach Center Publications

In this paper we deal with the energy functionals for the elastic thin film ω ⊂ ℝ² involving the bending moments. The effective energy functional is obtained 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 to be non-power-growth-type and to satisfy the conditions Δ₂ and...

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

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 to be non-power-growth-type...

Elliptic boundary value problem in Vanishing Mean Oscillation hypothesis

Maria Alessandra Ragusa (1999)

Commentationes Mathematicae Universitatis Carolinae

In this note the well-posedness of the Dirichlet problem (1.2) below is proved in the class H 0 1 , p ( Ω ) for all 1 < p < and, as a consequence, the Hölder regularity of the solution u . is an elliptic second order operator with discontinuous coefficients ( V M O ) and the lower order terms belong to suitable Lebesgue spaces.

Elliptic Systems of Pseudodifferential Equations in the Refined Scale on a Closed Manifold

Vladimir A. Mikhailets, Aleksandr A. Murach (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

We study a system of pseudodifferential equations which is elliptic in the Petrovskii sense on a closed smooth manifold. We prove that the operator generated by the system is a Fredholm operator in a refined two-sided scale of Hilbert function spaces. Elements of this scale are special isotropic spaces of Hörmander-Volevich-Paneah.

Embedding theorems for anisotropic Lipschitz spaces

F. J. Pérez (2005)

Studia Mathematica

Anisotropic Lipschitz spaces are considered. For these spaces we obtain sharp embeddings in Besov and Lorentz spaces. The methods used are based on estimates of iterative rearrangements. We find a unified approach that arises from the estimation of functions defined as minimum of a given system of functions. The case of L¹-norm is also covered.

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