H convergence for quasi-linear elliptic equations with quadratic growth

A. Bensoussan; L. Boccardo; F. Murat

doi:10.1007/BF01371084

H convergence for quasi-linear elliptic equations with quadratic growth

A. Bensoussan, L. Boccardo, F. Murat

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

26 Citations (Scopus)

Abstract

We consider in this paper the limit behavior of the solutions u^e{open} of the problem {Mathematical expression} where H^e{open} has quadratic growth in Du^e{open} and a^e{open}(x) is a family of matrices satisfying the general assumptions of abstract homogenization. We also consider the problem {Mathematical expression} where G^e{open} has quadratic growth in Du^e{open} and satisfies G^e{open}(x, s, ξ)s ≥ 0. Note that in this last model u^e{open} is in general unbounded, which gives extra difficulties for the homogenization process. In both cases we pass to the limit and obtain an homogenized equation having the same structure. © 1992 Springer-Verlag New York Inc.

Original language	English
Pages (from-to)	253-272
Journal	Applied Mathematics & Optimization
Volume	26
Issue number	3
DOIs	https://doi.org/10.1007/BF01371084
Publication status	Published - Nov 1992
Externally published	Yes

Research Keywords

G-convergence
H-convergence
Homogenization
Quasi-linear PDE

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title = "H convergence for quasi-linear elliptic equations with quadratic growth",

abstract = "We consider in this paper the limit behavior of the solutions ue{open} of the problem {Mathematical expression} where He{open} has quadratic growth in Due{open} and ae{open}(x) is a family of matrices satisfying the general assumptions of abstract homogenization. We also consider the problem {Mathematical expression} where Ge{open} has quadratic growth in Due{open} and satisfies Ge{open}(x, s, ξ)s ≥ 0. Note that in this last model ue{open} is in general unbounded, which gives extra difficulties for the homogenization process. In both cases we pass to the limit and obtain an homogenized equation having the same structure. {\textcopyright} 1992 Springer-Verlag New York Inc.",

keywords = "G-convergence, H-convergence, Homogenization, Quasi-linear PDE",

author = "A. Bensoussan and L. Boccardo and F. Murat",

year = "1992",

month = nov,

doi = "10.1007/BF01371084",

language = "English",

volume = "26",

pages = "253--272",

journal = "Applied Mathematics & Optimization",

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TY - JOUR

T1 - H convergence for quasi-linear elliptic equations with quadratic growth

AU - Bensoussan, A.

AU - Boccardo, L.

AU - Murat, F.

PY - 1992/11

Y1 - 1992/11

N2 - We consider in this paper the limit behavior of the solutions ue{open} of the problem {Mathematical expression} where He{open} has quadratic growth in Due{open} and ae{open}(x) is a family of matrices satisfying the general assumptions of abstract homogenization. We also consider the problem {Mathematical expression} where Ge{open} has quadratic growth in Due{open} and satisfies Ge{open}(x, s, ξ)s ≥ 0. Note that in this last model ue{open} is in general unbounded, which gives extra difficulties for the homogenization process. In both cases we pass to the limit and obtain an homogenized equation having the same structure. © 1992 Springer-Verlag New York Inc.

AB - We consider in this paper the limit behavior of the solutions ue{open} of the problem {Mathematical expression} where He{open} has quadratic growth in Due{open} and ae{open}(x) is a family of matrices satisfying the general assumptions of abstract homogenization. We also consider the problem {Mathematical expression} where Ge{open} has quadratic growth in Due{open} and satisfies Ge{open}(x, s, ξ)s ≥ 0. Note that in this last model ue{open} is in general unbounded, which gives extra difficulties for the homogenization process. In both cases we pass to the limit and obtain an homogenized equation having the same structure. © 1992 Springer-Verlag New York Inc.

KW - G-convergence

KW - H-convergence

KW - Homogenization

KW - Quasi-linear PDE

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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0005271059&origin=recordpage

U2 - 10.1007/BF01371084

DO - 10.1007/BF01371084

M3 - RGC 21 - Publication in refereed journal

SN - 0095-4616

VL - 26

SP - 253

EP - 272

JO - Applied Mathematics & Optimization

JF - Applied Mathematics & Optimization

IS - 3

ER -

H convergence for quasi-linear elliptic equations with quadratic growth

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