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Let X be a Banach space and X'
its continuous dual. C(X) (resp. C(X')) denotes the set of nonempty convex closed subsets of X
(resp. ω*-closed subsets of X') endowed with the topology
of uniform convergence of distance functions on bounded sets. This topology
reduces to the Hausdorff metric topology on the closed and bounded convex
sets [16] and in general has a Hausdorff-like presentation [11]. Moreover,
this topology is well suited for estimations and constructive approximations [6-9].
We...
In the 1950’s and 1960’s surface physicists/metallurgists such as Herring and Mullins applied ingenious thermodynamic arguments to explain a number of experimentally observed surface phenomena in crystals. These insights permitted the successful engineering of a large number of alloys, where the major mathematical novelty was that the surface response to external stress was anisotropic. By examining step/terrace (vicinal) surface defects it was discovered through lengthy and tedious experiments...
In the 1950's and 1960's surface physicists/metallurgists such as
Herring and Mullins applied ingenious thermodynamic arguments to explain a
number of experimentally observed surface phenomena in crystals. These insights permitted
the successful engineering of a large number of alloys, where the
major mathematical novelty was that the surface response to external stress was anisotropic.
By examining step/terrace (vicinal) surface defects it was discovered through
lengthy and tedious experiments...
We consider applications, illustration and concrete numerical treatments of some homogenization results on Stokes flow in porous media. In particular, we compute the global permeability tensor corresponding to an unidirectional array of circular fibers for several volume-fractions. A 3-dimensional problem is also considered.
We construct a guided continuous selection for lsc multifunctions with decomposable values in L¹[0,T]. We then apply it to obtain a new result on the uniform approximation of relaxed solutions for lsc differential inclusions.
Integral representation of relaxed energies and of
Γ-limits of functionals
are obtained when sequences of fields v may develop oscillations and are
constrained to satisfy
a system of first order linear partial differential equations. This
framework includes the
treatement of divergence-free fields, Maxwell's equations in
micromagnetics, and curl-free
fields. In the latter case classical relaxation theorems in W1,p, are
recovered.
We consider the problem of placing a Dirichlet region made by n small balls of given radius in a given domain subject to a force f in order to minimize the compliance of the configuration. Then we let n tend to infinity and look for the Γ-limit of suitably scaled functionals, in order to get informations on the asymptotical distribution of the centres of the balls. This problem is both linked to optimal location and shape optimization problems.
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