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Asymptotic study of a nonlinear elliptic boundary Steklov problem on a nanostructure

Maadan Hicham, Messaho Jamal

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20240076

The present study is related to the existence and the asymptotic behavior of the solution of a nonlinear elliptic Steklov problem imposed on a nanostructure depending on the thickness parameter ε (nano-scale), distributed on the boundary of the domain when the parameter ε goes to 0, under some appropriate conditions on the data involved in the problem. We use epi-convergence method in order to establish the limit behavior by characterizing the weak limits of the energies for the solutions. An intermediate step in the proof provides a homogenization result for the considered structure.