1,721,030 research outputs found
On lower semicontinuity in BHp and 2-quasiconvexification
No full textIt is proved that if u ∈ BHp(Ω;Rd), with p > 1, if {un} is bounded in BHp(Ω; Rd), |Ds2un|(Ω) → 0, and if un → u in W1, 1(Ω; Rd), then ∫ Ω f(x, u(x), ∇u(x), ∇2u(x)), dx ≤ lim infn→+∞ ∫Ω f(x, un (x), ∇un(x), ∇2un(x)) dx provided f(x, u, ξ, ·) is 2-quasiconvex and satisfies some appropriate growth and continuity condition. Characterizations of the 2-quasiconvex envelope when admissible test functions belong to BHP are provided
A relaxation theorem in the space of functions of bounded deformation
Get PDFWe obtain an integral representation for the relaxation, in the space of functions of bounded deformation, of an energy satifying certain growth and coercivity conditions
Shapes of Epitaxially Grown Quantum Dots
Get PDFA variational model introduced by Spencer and Tersoff (Appl. Phys. Lett. 96:073114, 2010) to describe optimal faceted shapes of epitaxially deposited films is studied analytically in the case in which there are a non-vanishing crystallographic miscut and a lattice incompatibility between the film and the substrate. The existence of faceted minimizers for every volume of the deposited film is established. In particular, it is shown that there is no wetting effect for small volumes. Geometric properties including a faceted version of the zero contact angle are derived, and the explicit shapes of minimizers for small volumes are identified
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
A note on Meyers' theorem in Wk,1
No full textLower semicontinuity properties of multiple integrals u â Wk,1(Ω;âd) â â«Î© f (x,u(x), â ̄, âku(x)) dx are studied when f may grow linearly with respect to the highest-order derivative, âku, and admissible Wk,1(Ω;âd) sequences converge strongly in Wk-l,1(Ω;âd). It is shown that under certain continuity assumptions on f, convexity, 1-quasiconvexity or k-polyconvexity of Î3⁄4 â f(x0, u(x0), â ̄, âk-1u(x0), Î3⁄4) ensures lower semicontinuity. The case where f(x0, u(x0), â ̄ , âk-1u(x0),·) is k-quasiconvex remains open except in some very particular cases, such as when f(x, u(x), â ̄ , âku(x)) = h(x)g(âku(x))
Equilibria and dislocations in epitaxial growth
No full textAn overview of recent analytical developments in epitaxial growth is presented. The energy release via the onset of dislocations is addressed. Regularity of quasistatic equilibria is studied both in the absence and in the presence of dislocations. Morphological evolution of anisotropic epitaxially strained films is considered under the assumption that the surface evolves by surface diffusion under the influence of a chemical potential
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