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Homogenization of quasilinear problems with semilinear terms and Signorini boundary conditions in perforated domains

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Abstract

This paper studies the upscaling of an elliptic problem with a highly oscillating quasilinear matrix coefficient, a quasilinear term, and a semilinear term in domains periodically perforated with holes of critical size. A Signorini boundary condition is imposed on the boundary of the holes, while a Dirichlet boundary condition is prescribed on the exterior boundary. Using the periodic unfolding method, we obtain an obstacle problem with a nonnegativity spreading effect.

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Acknowledgements

This work was carried out independently during the sandwich program of the author at the University of Salerno, Italy with financial support from the University of the Philippines through the Office of the Vice President for Academics Affairs via the UP System Faculty, REPS and Administrative Staff Development Program. The author also thanks the Office of the Chancellor of the University of the Philippines Diliman, through the Office of the Vice Chancellor for Research and Development, for additional funding support through the Thesis and Dissertation Grant.

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  1. Institute of Mathematics, University of the Philippines Diliman, 1101, Diliman, Quezon City, Philippines

    Jake Avila

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Avila, J. Homogenization of quasilinear problems with semilinear terms and Signorini boundary conditions in perforated domains. Nonlinear Differ. Equ. Appl. 31, 64 (2024). https://doi.org/10.1007/s00030-024-00957-0

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