Homogenization for conductive thin layers of pre-fractal type

The aim of this work is to obtain convergence results for the solutions of transmission problems across highly conductive layers of pre-fractal type from the point of view of homogenization. We prove the M-convergence of the energy functionals to an energy functional which incorporates a singular term, supported within the layer. From the convergence of the energy functionals we deduce the convergence of the approximating solutions to the limit solution in a suitable sense.

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