The authors prove Gamma-convergence of nonlocal convolution-type energies on thin domains to a local lower-dimensional integral functional, with the limit energy density given by an asymptotic formula depending on the relative scaling of epsilon and gamma.
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Multiscale analysis and homogenization of nonlocal thin films
The authors prove Gamma-convergence of nonlocal convolution-type energies on thin domains to a local lower-dimensional integral functional, with the limit energy density given by an asymptotic formula depending on the relative scaling of epsilon and gamma.