2018
DOI: 10.1051/cocv/2017026
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Unilateral problems for thep-Laplace operator in perforated media involving large parameters

Abstract: Abstract. We address homogenization problems for variational inequalities issue from unilateral constraints for the p-Laplacian posed in perforated domains of R n , with n ≥ 3 and p ∈ [2, n]. ε is a small parameter which measures the periodicity of the structure while aε ε measures the size of the perforations. We impose constraints for solutions and their fluxes (associated with the p-Laplacian) on the boundary of the perforations. These constraints imply that the solution is positive and that the flux is bou… Show more

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Cited by 16 publications
(15 citation statements)
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“…Even when p is equal to 2, models (11) and (47) are not considered in the literature for the nonlinear functions g and h given by (12b), (12c) and (48). Taking into account the general idea of this paper for the p-Laplacian, the constraints and the technique, the closest paper in the literature is [5]. In spite of this, [5] deals with different geometrical configuration since the cavities are distributed over the whole domain: cf.…”
Section: Introductionmentioning
confidence: 99%
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“…Even when p is equal to 2, models (11) and (47) are not considered in the literature for the nonlinear functions g and h given by (12b), (12c) and (48). Taking into account the general idea of this paper for the p-Laplacian, the constraints and the technique, the closest paper in the literature is [5]. In spite of this, [5] deals with different geometrical configuration since the cavities are distributed over the whole domain: cf.…”
Section: Introductionmentioning
confidence: 99%
“…Taking into account the general idea of this paper for the p-Laplacian, the constraints and the technique, the closest paper in the literature is [5]. In spite of this, [5] deals with different geometrical configuration since the cavities are distributed over the whole domain: cf. also [2,3,13,14,15,20,22,24] for perforated domains over the whole volume.…”
Section: Introductionmentioning
confidence: 99%
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“…Мы также упоминаем работы, в которых аналогичная задача была изучена для перфорированных областей с нелинейным краевым условием типа Робина, заданным на границе полостей, см. [8][9][10][11][12][13][14].…”
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