A mass-at-infinity functional unifies the Maz'ya-Shaposhnikova limit with fractional perimeter asymptotics for non-integrable functions on Lipschitz domains.
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As s approaches 0, nonlocal minimal graphs in the obstacle problem adhere completely to the obstacle and leave the domain asymptotically empty, providing counterexamples to continuity.
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Closing the gap: Maz'ya-Shaposhnikova and asymptotics of fractional perimeters
A mass-at-infinity functional unifies the Maz'ya-Shaposhnikova limit with fractional perimeter asymptotics for non-integrable functions on Lipschitz domains.
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Asymptotics as $s\searrow 0$ of the nonlocal nonparametric Plateau problem with obstacles
As s approaches 0, nonlocal minimal graphs in the obstacle problem adhere completely to the obstacle and leave the domain asymptotically empty, providing counterexamples to continuity.