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-convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness approaches zero of a ferromagnetic thin structure , , whose energy is given bysubject toand to the constraintwhere is any continuous function satisfying -growth assumptions with . Partial results are also obtained in the case , under an additional assumption on .
Γ-convergence techniques and relaxation results of
constrained energy functionals are used to identify the limiting energy as the
thickness ε approaches zero of a ferromagnetic thin
structure , , whose
energy is given by
subject to
and to the constraint
where W is any continuous function satisfying p-growth assumptions
with p> 1.
Partial results are also obtained in the case p=1, under
an additional assumption on W.
In this paper, we prove that the approximants naturally associated to a supremal functional -converge to it. This yields a lower semicontinuity result for supremal functionals whose supremand satisfy weak coercivity assumptions as well as a generalized Jensen inequality. The existence of minimizers for variational problems involving such functionals (together with a Dirichlet condition) then easily follows. In the scalar case we show the existence of at least one absolute minimizer (i.e. local...
In this paper, we use -convergence techniques to study the following variational problemwhere , with , and is a bounded domain of , . We obtain a -convergence result, on which one can easily read the usual concentration phenomena arising in critical growth problems. We extend the result to a non-homogeneous version of problem . Finally, a second order expansion in -convergence permits to identify the concentration points of the maximizing sequences, also in some non-homogeneous case.
Given an open, bounded and connected set with Lipschitz boundary and volume , we prove that the sequence of Dirichlet functionals defined on , with volume constraints on fixed level-sets, and such that for all , -converges, as with , to the squared total variation on , with as volume constraint on the same level-sets.
The numerical approximation of the minimum problem: , is considered, where . The solution to this problem is a set with prescribed mean curvature and contact angle at the intersection of with . The functional is first relaxed with a sequence of nonconvex functionals defined in which, in turn, are discretized by finite elements. The -convergence of the discrete functionals to as well as the compactness of any sequence of discrete absolute minimizers are proven.
In this note we give a nonstandard characterization of multiple topological operators as sup-min of standard part map.
The notion of -limit is extended from the case of functions with values in to the case of those with values in an arbitrary complete lattice and the problem of convergence of Pareto minima related to a convex cone is considered.
In this paper, we prove that the Lp approximants naturally associated to a supremal functional
Γ-converge to it. This yields a lower semicontinuity result for supremal
functionals whose supremand satisfy weak coercivity assumptions as
well as a generalized Jensen inequality. The existence of minimizers
for variational problems involving such functionals (together with a
Dirichlet condition) then easily follows. In the scalar
case we show the existence of at least one absolute minimizer (i.e. local
solution)...
We study the stability of a sequence of integral
functionals on divergence-free matrix valued fields following the direct
methods of Γ-convergence. We prove that the Γ-limit
is an integral functional on divergence-free matrix valued fields.
Moreover, we show that the Γ-limit is also stable under
volume constraint and various type of boundary conditions.
We compute the Γ-limit of a sequence of non-local integral functionals depending on a regularization of the gradient term by means of a convolution kernel. In particular, as Γ-limit, we obtain free discontinuity functionals with linear growth and with anisotropic surface energy density.
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