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Asymptotic analysis of a semilinear elliptic equation in highly oscillating thin domains

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Abstract

In this work we are interested in the asymptotic behavior of a family of solutions of a semilinear elliptic problem with homogeneous Neumann boundary condition defined in a two-dimensional bounded set which degenerates to the unit interval as a positive parameter \({\epsilon}\) goes to zero. Here we also allow that upper and lower boundaries from this singular region present highly oscillatory behavior with different orders and variable profile. Combining results from linear homogenization theory and nonlinear analyzes we get the limit problem showing upper and lower semicontinuity of the solutions at \({\epsilon=0}\).

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-090, São Paulo, SP, Brazil

    Marcone Corrêa Pereira

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  1. Marcone Corrêa Pereira
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Correspondence to Marcone Corrêa Pereira.

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Partially supported by FAPESP 2013/22275-1, CNPq 302960/2014-7 and 471210/2013-7, Brazil.

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Pereira, M.C. Asymptotic analysis of a semilinear elliptic equation in highly oscillating thin domains. Z. Angew. Math. Phys. 67, 134 (2016). https://doi.org/10.1007/s00033-016-0727-y

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  • DOI: https://doi.org/10.1007/s00033-016-0727-y

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