Loading [MathJax]/jax/output/SVG/jax.js
Search Advanced

Networks and Heterogeneous Media

2008, Volume 3, Issue 3: 489-508. doi: 10.3934/nhm.2008.3.489
Previous Article Next Article

Non convex homogenization problems for singular structures

  • 1.
    Dipartimento di Matematica, Università di Roma 'Tor Vergata', via della Ricerca Scientifica, 00133 Roma
  • 2.
    Department of mathematical sciences, Politecnico, Torino, Corso Duca degli Abruzzi 24, 10129 Torino
  • Received: 01 March 2008

  • Primary: 74Q15, 49J45; Secondary: 35B27.

  • We prove a homogenization theorem for non-convex functionals depending on vector-valued functions, defined on Sobolev spaces with respect to oscillating measures. The proof combines the use of the localization methods of Γ-convergence with a 'discretization' argument, which allows to link the oscillating energies to functionals defined on a single Lebesgue space, and to state the hypothesis of p-connectedness of the underlying periodic measure in a handy way.

    Citation: Andrea Braides, Valeria Chiadò Piat. Non convex homogenization problems for singular structures[J]. Networks and Heterogeneous Media, 2008, 3(3): 489-508. doi: 10.3934/nhm.2008.3.489

    Related Papers:

    [1] Andrea Braides, Valeria Chiadò Piat . Non convex homogenization problems for singular structures. Networks and Heterogeneous Media, 2008, 3(3): 489-508. doi: 10.3934/nhm.2008.3.489
    [2] Antoine Gloria Cermics . A direct approach to numerical homogenization in finite elasticity. Networks and Heterogeneous Media, 2006, 1(1): 109-141. doi: 10.3934/nhm.2006.1.109
    [3] T. A. Shaposhnikova, M. N. Zubova . Homogenization problem for a parabolic variational inequality with constraints on subsets situated on the boundary of the domain. Networks and Heterogeneous Media, 2008, 3(3): 675-689. doi: 10.3934/nhm.2008.3.675
    [4] Patrick Henning . Convergence of MsFEM approximations for elliptic, non-periodic homogenization problems. Networks and Heterogeneous Media, 2012, 7(3): 503-524. doi: 10.3934/nhm.2012.7.503
    [5] Vivek Tewary . Combined effects of homogenization and singular perturbations: A bloch wave approach. Networks and Heterogeneous Media, 2021, 16(3): 427-458. doi: 10.3934/nhm.2021012
    [6] Erik Grandelius, Kenneth H. Karlsen . The cardiac bidomain model and homogenization. Networks and Heterogeneous Media, 2019, 14(1): 173-204. doi: 10.3934/nhm.2019009
    [7] Leonid Berlyand, Volodymyr Rybalko . Homogenized description of multiple Ginzburg-Landau vortices pinned by small holes. Networks and Heterogeneous Media, 2013, 8(1): 115-130. doi: 10.3934/nhm.2013.8.115
    [8] Junlong Chen, Yanbin Tang . Homogenization of nonlinear nonlocal diffusion equation with periodic and stationary structure. Networks and Heterogeneous Media, 2023, 18(3): 1118-1177. doi: 10.3934/nhm.2023049
    [9] Ben Schweizer, Marco Veneroni . The needle problem approach to non-periodic homogenization. Networks and Heterogeneous Media, 2011, 6(4): 755-781. doi: 10.3934/nhm.2011.6.755
    [10] Mohamed Camar-Eddine, Laurent Pater . Homogenization of high-contrast and non symmetric conductivities for non periodic columnar structures. Networks and Heterogeneous Media, 2013, 8(4): 913-941. doi: 10.3934/nhm.2013.8.913
  • We prove a homogenization theorem for non-convex functionals depending on vector-valued functions, defined on Sobolev spaces with respect to oscillating measures. The proof combines the use of the localization methods of Γ-convergence with a 'discretization' argument, which allows to link the oscillating energies to functionals defined on a single Lebesgue space, and to state the hypothesis of p-connectedness of the underlying periodic measure in a handy way.


  • This article has been cited by:

    1. Omar Anza Hafsa, Jean-Philippe Mandallena, Γ-convergence of nonconvex integrals in Cheeger--Sobolev spaces and homogenization, 2017, 10, 1864-8266, 381, 10.1515/acv-2015-0053
    2. Andrea Braides, Lorenza D’Elia, Homogenization of discrete thin structures, 2022, 0362546X, 112951, 10.1016/j.na.2022.112951
    3. Andrea Braides, Andrea Cancedda, Valeria Chiadò Piat, Homogenization of metrics in oscillating manifolds, 2017, 23, 1292-8119, 889, 10.1051/cocv/2016018
    4. Andrea Braides, Valeria Chiadò Piat, Homogenization of networks in domains with oscillating boundaries, 2019, 98, 0003-6811, 45, 10.1080/00036811.2018.1430782
  • Reader Comments
  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Networks and Heterogeneous Media
1.3 1.9

Metrics

Article views(3602) PDF downloads(85) Cited by(4)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog