Homogenization of unbounded integrals with quasiconvex growth

Hafsa, Omar Anza; Mandallena, Jean-Philippe; Zorgati, Hamdi

doi:10.1007/s10231-014-0437-z

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2023

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Cited by 5 publications

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“…Later, this concept was proved very useful for relaxation problems in the vectorial case with bounded and convex constraints see [AH10]. Then, it was used to study homogenization and relaxation problems with constraints (see for instance [AHM11,AHM12,AHMZ15]). Ru-usc seems to be a key concept to deal with certain constrained variational problems (see Sect.…”

Section: Introductionmentioning

confidence: 99%

Radial extension of $${\Gamma }$$-limits

Hafsa

Mandallena

2023

Boll Unione Mat Ital

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We continue in this paper our study of the notion of radial uniformly upper semicontinuous functional that we developed in a previous paper (see [AHM14]) in the context of relaxation. We consider here the framework of Γ-convergence. We present general radial extension results with respect to Γ-convergence and give some applications to Γconvergence and homogenization of integral functionals with constraints.

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Section: Introductionmentioning

confidence: 99%

Radial extension of $${\Gamma }$$-limits

Hafsa

Mandallena

2023

Boll Unione Mat Ital

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Integral representation of unbounded variational functionals on Sobolev spaces

Hafsa

Mandallena

2021

Ricerche mat

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A. In this paper we establish an unbounded version of the integral representation theorem by Buttazzo and Dal Maso (see [BDM85] and also [BFLM02]). More precisely, we prove an integral representation theorem (with a formula for the integrand) for functionals de ned on W 1,p with p ą N (N being the dimension) that do not satisfy a standard p-growth condition from above and can take in nite values. Applications to Γ-convergence, relaxation and homogenization are also developed.

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