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On the homogenization of weakly nonlinear divergent operators in a perforated cube

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Abstract

In the present paper we consider a second order weakly nonlinear elliptic equation of divergent form with a lower term growing at infinity (with respect to the unknown function) as a power function. It is proved that a sequence of solutions in the perforated cubes converges to a solution in the nonperforated cube as the diameters of the holes tends to zero, and the rate of convergence depends on the power exponent of the lower term.

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References

  1. V. A. Marchenko and E. Ya. Khruslov,Boundary-Value Problems with Finely Granulated Boundaries [in Russian], Naukova Dumka, Kiev (1974).

    Google Scholar 

  2. A. Bensoussan, J.-L. Lions, and G. Papanicolaou,Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam (1978).

    MATH  Google Scholar 

  3. A. Damlamian and Li Ta-Tsien, “Boundary homogenization for elliptic problems,”J. Math. Pures et Appl.,66, 351–361 (1987).

    MATH  Google Scholar 

  4. V. V. Zhikov, S. M. Kozlov, and O. A. Oleinik,Homogenization of Differential Operators [in Russian], Fizmatlit, Moscow (1993).

    MATH  Google Scholar 

  5. I. V. Skripnik,Methods of Investigation of Nonlinear Elliptic Boundary-Value Problems [in Russian], Fizmatlit, Moscow (1990).

    Google Scholar 

  6. V. A. Kondrat’ev and E. M. Landis, “On the qualitative properties of solutions of one nonlinear second order equation,”Mat. Sb. [Russian Acad. Sci. Sb. Math.],135, No. 3, 346–360 (1988).

    Google Scholar 

  7. V. A. Kondrat’ev and E. M. Landis, “Semilinear equations of second order with nonnegative characteristics form,”Mat. Zametki [Math. Notes],44, No. 4, 457–468 (1988).

    Google Scholar 

  8. M. V. Tuvaev, “On removable singularity sets of solutions of quasilinear elliptic equations,”Mat. Sb. [Russian Acad. Sci. Sb. Math.],185, No. 2, 107–114 (1994).

    Google Scholar 

  9. J. L. Vazques and L. Veron, “Removable singularities of strongly nonlinear elliptic equations,”Manuscripta Math.,33, 129–144 (1980/81).

    Article  Google Scholar 

  10. J. L. Vazques and L. Veron, “Singularities of elliptic equations with an exponential nonlinearity,”Math. Anal.,269, 119–135 (1984).

    Article  Google Scholar 

  11. J. L. Vazques and L. Veron, “Isolated singularities of some semilinear elliptic equations,”Journal of Diff. Equations,60, 301–322 (1985).

    Article  Google Scholar 

  12. W. Littman, G. Stampacchia, and B. Weinberger, “Regular points for elliptic equations with discontinuous coefficients,”Ann. Scuola Norm. Super. Pisa. Ser. 3,17, No. 1-2, 43–77 (1963).

    MATH  Google Scholar 

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow, USSR

    H. A. Matevossian & S. V. Pikouline

Authors
  1. H. A. Matevossian
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  2. S. V. Pikouline
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Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 390–398, September, 2000.

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Matevossian, H.A., Pikouline, S.V. On the homogenization of weakly nonlinear divergent operators in a perforated cube. Math Notes 68, 337–344 (2000). https://doi.org/10.1007/BF02674557

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  • DOI: https://doi.org/10.1007/BF02674557

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