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Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 2
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Original Articles

Averaging of variational inequalities for the Laplacian with nonlinear restrictions along manifolds

D. Gómez Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain
,
M. Lobo Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, 39005 Santander, Spain
,
M.E. Pérez Departamento de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, 39005 Santander, SpainCorrespondence[email protected]
&
T.A. Shaposhnikova Department of Differential Equations, Moscow State University, 119992 Moscow, Russia
Pages 218-237 | Received 16 May 2011, Accepted 29 Jun 2011, Published online: 19 Aug 2011

Citations (18)

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Read on this site (2)

D. Gómez, M. Lobo, E. Pérez & E. Sanchez-Palencia. (2018) Homogenization in perforated domains: a Stokes grill and an adsorption process. Applicable Analysis 97:16, pages 2893-2919.
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A. Brillard, D. Gómez, M. Lobo, E. Pérez & T. A. Shaposhnikova. (2016) Boundary homogenization in perforated domains for adsorption problems with an advection term. Applicable Analysis 95:7, pages 1517-1533.
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Articles from other publishers (16)

Denis Ivanovich Borisov & Albina Ishbuldovna Mukhametrakhimova. (2022) Asymptotics for problems in perforated domains with Robin nonlinear condition on the boundaries of cavities. Sbornik: Mathematics 213:10, pages 1318-1371.
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Denis Ivanovich Borisov & Albina Ishbuldovna Mukhametrakhimova. (2022) Асимптотики для задач в перфорированных областях с третьим нелинейным краевым условием на границах полостейAsymptotics for problems in perforated domains with Robin nonlinear condition on the boundaries of cavities. Математический сборник Matematicheskii Sbornik 213:10, pages 3-59.
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D. I. Borisov & A. I. Mukhametrakhimova. (2021) Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition. Sbornik: Mathematics 212:8, pages 1068-1121.
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Denis Ivanovich Borisov & Albina Ishbuldovna Mukhametrakhimova. (2021) Равномерная сходимость и асимптотики для задач в областях с мелкой перфорацией вдоль заданного многообразия в случае усредненного условия ДирихлеUniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition. Математический сборник Matematicheskii Sbornik 212:8, pages 33-88.
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Jesús Ildefonso Díaz, David Gómez-Castro, Alexander V. Podolskiy & Tatiana A. Shaposhnikova. (2020) Homogenization of a net of periodic critically scaled boundary obstacles related to reverse osmosis “nano-composite” membranes. Advances in Nonlinear Analysis 9:1, pages 193-227.
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D. Gómez, E. Pérez, A. V. Podolskii & T. A. Shaposhnikova. (2017) Homogenization of Variational Inequalities for the p-Laplace Operator in Perforated Media Along Manifolds. Applied Mathematics & Optimization 79:3, pages 695-713.
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Tiziana Durante. Homogenization of elliptic operators in a strip perforated along a curve. Homogenization of elliptic operators in a strip perforated along a curve.
T. A. Shaposhnikova & M. N. Zubova. (2018) Homogenization of Variational Inequality for the Laplace Operator with Nonlinear Constraint on the Flow in a Domain Perforated by Arbitrary Shaped Sets. Critical Case. Journal of Mathematical Sciences 232:4, pages 573-590.
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J. I. Díaz, D. Gómez-Castro, A. V. Podolskiy & T. A. Shaposhnikova. (2018) Homogenization of Boundary Value Problems in Plane Domains with Frequently Alternating Type of Nonlinear Boundary Conditions: Critical Case. Doklady Mathematics 97:3, pages 271-276.
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Delfina Gómez, Miguel Lobo, Eugenia Pérez, Alexander V. Podolskii & Tatiana A. Shaposhnikova. (2018) Unilateral problems for the p -Laplace operator in perforated media involving large parameters . ESAIM: Control, Optimisation and Calculus of Variations 24:3, pages 921-964.
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A. V. Podolskiy & T. A. Shaposhnikova. (2018) Homogenization of the boundary value problem for the Laplace operator in a domain perforated along (n – 1)-dimensional manifold with nonlinear Robin type boundary condition on the boundary of arbitrary shaped holes: Critical case. Doklady Mathematics 96:3, pages 601-606.
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А.В. Подольский & Т.А. Шапошникова. (2017) УСРЕДНЕНИЕ КРАЕВОЙ ЗАДАЧИ ДЛЯ ОПЕРАТОРА ЛАПЛАСА В ОБЛАСТИ, ПЕРФОРИРОВАННОЙ ВДОЛЬ (N - 1)-МЕРНОГО МНОГООБРАЗИЯ, С НЕЛИНЕЙНЫМ КРАЕВЫМ УСЛОВИЕМ РОБИНА НА ГРАНИЦЕ ПОЛОСТЕЙ ПРОИЗВОЛЬНОЙ ФОРМЫ: КРИТИЧЕСКИЙ СЛУЧАЙ, "Доклады Академии наук". Доклады Академии Наук:5, pages 516-522.
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J. I. Diaz, D. Gómez-Castro, A. V. Podol’skii & T. A. Shaposhnikova. (2016) Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators. Doklady Mathematics 94:1, pages 387-392.
Crossref
D. Gómez, M. Lobo, M. E. Pérez, T. A. Shaposhnikova & M. N. Zubova. (2014) On critical parameters in homogenization of perforated domains by thin tubes with nonlinear flux and related spectral problems. Mathematical Methods in the Applied Sciences 38:12, pages 2606-2629.
Crossref
A. V. Podol’skiy & T. A. Shaposhnikova. (2015) Homogenization for the p-Laplacian in an n-dimensional domain perforated by very thin cavities with a nonlinear boundary condition on their Boundary in the case p = n. Doklady Mathematics 92:1, pages 464-470.
Crossref
D. Gómez, M. E. Pérez, A. V. Podolskiy & T. A. Shaposhnikova. (2015) Homogenization for the p-Laplace operator in perforated media with nonlinear restrictions on the boundary of the perforations: A critical Case. Doklady Mathematics 92:1, pages 433-438.
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