| Abstract: |
| We investigate the asymptotic behavior of anisotropic fractional energies as the fractional parameter $s \in (0, 1)$ approaches the critical limits $s \uparrow 1$ and $s \downarrow 0$, in the spirit of the seminal works by Bourgain-Brezis-Mironescu and Maz`ya-Shaposhnikova. Focusing on the limit $s \uparrow 1$, we analyze the stability and convergence of solutions to the corresponding minimization problems.
Finally, we examine the interplay between homogenization effects and the localization phenomena that arise as the operator recovers its local structure in the limit $s \uparrow 1$. |
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