Homogenization of almost periodic monotone operators

Braides, Andrea; Piat, Valeria Chiadò; Defranceschi, Anneliese

doi:10.1016/s0294-1449(16)30233-5

Cited by 40 publications

(47 citation statements)

References 18 publications

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“…Moreover, our assumption (A4) clarifies the problems with general (x, y)-dependent maximal monotone maps g: utilizing maximal monotonicity in function spaces is limited by the fact that test-functions must be admissible in the sense of two-scale convergence. Indeed, the properties of maximal monotone operators in periodic homogenization problems require careful analysis, and we additionally refer to [6,9,10,12,14].…”

Section: Further Comparison With the Literaturementioning

confidence: 99%

Homogenization of plasticity equations with two-scale convergence methods

Schweizer

Veneroni

2014

Applicable Analysis

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We investigate the deformation of heterogeneous plastic materials. The model uses internal variables and kinematic hardening, elastic and plastic strain are used in an infinitesimal strain theory. For periodic material properties with periodicity length scale η > 0, we obtain the limiting system as η → 0. The limiting two-scale plasticity model coincides with well-known effective models. Our direct approach relies on abstract tools from two-scale convergence (regarding convex functionals and monotone operators) and on higher order estimates for solution sequences.

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Section: Further Comparison With the Literaturementioning

confidence: 99%

Homogenization of plasticity equations with two-scale convergence methods

Schweizer

Veneroni

2014

Applicable Analysis

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“…In the case when the equation is monotone, with a(x="; ru " ) almost-periodic in the rst variable, the homogenization of (5.1) has been done in Braides et al (1992), using approximation results in smoother almost-periodic spaces. Corrector results for these operators are proved in Braides (1991), exploiting the geometric properties of a.…”

Section: Applications Of Homogenization Problemsmentioning

confidence: 99%

“…Corrector results for these operators are proved in Braides (1991), exploiting the geometric properties of a.…”

Section: Applications Of Homogenization Problemsmentioning

confidence: 99%

The two-scale convergence method applied to generalized Besicovitch spaces

Casado–Díaz

Gayte

2002

Proc. R. Soc. Lond. A

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The two-scale convergence method has proved to be a very useful tool for dealing with periodic homogenization problems. In the present paper we develop this theory to generalized Besicovitch spaces, which include the almost-periodic functions. The main di¯culty comes from the fact that these spaces are not separable. We also show how to apply these results to the homogenization of partial di¬erential problems in this framework.

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“…The homogenization of linear parabolic operators with almost periodic and random coefficients has been studied in [23,22]. We would like also to mention several results on homogenization of nonlinear elliptic operators [2,5,10,11,15,16]. We would like to note that general elliptic operators in divergence form are considered in [15,16], including random homogenization, while articles [2,5,10,11] are devoted to the homogenization of monotone second-order elliptic operators.…”

Section: Introductionmentioning

confidence: 99%

“…We would like also to mention several results on homogenization of nonlinear elliptic operators [2,5,10,11,15,16]. We would like to note that general elliptic operators in divergence form are considered in [15,16], including random homogenization, while articles [2,5,10,11] are devoted to the homogenization of monotone second-order elliptic operators. For general references in the field of homogenization, we refer to [1,3,6,7,12,17].…”

Section: Introductionmentioning

confidence: 99%