H convergence for quasi-linear elliptic equations with quadratic growth

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)253-272
Journal / PublicationApplied Mathematics & Optimization
Issue number3
Publication statusPublished - Nov 1992
Externally publishedYes


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.

Research Area(s)

  • G-convergence, H-convergence, Homogenization, Quasi-linear PDE