Nonlocal minimal surfaces are unique for all but countably many parameters in any strictly increasing family of exterior data, and arbitrarily small perturbations yield smooth minimizers in one dimension beyond the critical threshold.
3-4, 377–403, DOI 10.1007/s00229-010-0399-4
3 Pith papers cite this work, alongside 198 external citations. Polarity classification is still indexing.
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A mass-at-infinity functional unifies the Maz'ya-Shaposhnikova limit with fractional perimeter asymptotics for non-integrable functions on Lipschitz domains.
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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Nonlocal minimal surfaces are generically unique, and smooth in one extra dimension
Nonlocal minimal surfaces are unique for all but countably many parameters in any strictly increasing family of exterior data, and arbitrarily small perturbations yield smooth minimizers in one dimension beyond the critical threshold.
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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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How to Recognise Extension domains
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.