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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.
The work focuses on the Γ-convergence problem and the convergence of minimizers for a functional defined in a periodic perforated medium and
combining the bulk (volume distributed) energy and the surface
energy distributed on the perforation boundary. It is assumed that the mean value
of surface energy at each level set of test function is equal to
zero.
Under natural coercivity and p-growth assumptions on the bulk energy, and the assumption that the surface energy satisfies p-growth upper bound,...
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.
This paper is devoted to the homogenization beyond the periodic setting, of nonlinear monotone operators in a domain in with isolated holes of size ( a small parameter). The order of the size of the holes is twice that of the oscillations of the coefficients of the operator, so that the problem under consideration is a reiterated homogenization problem in perforated domains. The usual periodic perforation of the domain and the classical periodicity hypothesis on the coefficients of the operator...
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