| Abstract: |
| In this talk, we will introduce a nonlocal, variational model for thin films. We consider family of functionals of convolution-type defined on a thin domain of thickness $\gamma$ with the size of the most effective interactions between points being of order $\varepsilon$. After discussing the correct rescaling, we study the $\Gamma$-convergence of these energies as both parameters go to zero to a local integral functional defined on a lower dimensional domain. In the case of periodic homogenization, we can show that a separation of scales takes place.
This is a work in collaboration with Nadia Ansini. |
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