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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A bounded domain is a (1,p)-extension domain if and only if it is Ahlfors regular and satisfies (1-s)[f]_{W^{s,p}(Ω)}^p ≤ C [f]_{W^{1,p}(Ω)}^p for all f in the homogeneous Sobolev space and s near 1.
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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.