A mass-at-infinity functional unifies the Maz'ya-Shaposhnikova limit with fractional perimeter asymptotics for non-integrable functions on Lipschitz domains.
Fractional Calculus and Applied Analysis , year =
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Heat semigroup characterizes total variation for compactly supported BV on arbitrary smooth complete weighted Riemannian manifolds, with a counterexample on some weighted manifold.
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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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Sets of finite perimeter on Riemannian manifolds and stochastic completeness
Heat semigroup characterizes total variation for compactly supported BV on arbitrary smooth complete weighted Riemannian manifolds, with a counterexample on some weighted manifold.