Homogenization theorem establishing resolvent convergence of periodic convolution-type nonlocal operators to a homogenized operator comparable to the fractional Laplacian under Lévy tail assumptions.
Periodic and stochastic homogenization of general nonlocal operators with oscillating coefficients
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abstract
This paper investigates homogenization problems for the nonlocal operators with rapidly oscillating coefficients in the cases of periodic and random statistically homogeneous micro-structures. These operators involve the fractional Laplacian and some operators compared to it. Based on the $\Gamma$-convergence method and compactness arguments, we prove the homogenization theorems for these nonlocal operators with product-type and symmetric coefficient-structured kernels respectively. Furthermore, these results are extended to general nonlinear nonlocal equations.
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math.AP 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Periodic homogenization of convolution type operators with irregular L\'{e}vy type tails
Homogenization theorem establishing resolvent convergence of periodic convolution-type nonlocal operators to a homogenized operator comparable to the fractional Laplacian under Lévy tail assumptions.