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Towards a long-range theory of capillarity

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arxiv 2404.06705 v1 pith:OXDEKYFP submitted 2024-04-10 math.AP

Enrico Valdinoci This is my paper · ORCID
classification math.AP
keywords capillarityclassicallong-rangetheoryaccountingaimsangleapproach
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We recall the classical theory of capillarity, describing the shape of a liquid droplet in a container, and present a recent approach which aims at accounting for long-range particle interactions. This nonlocal setting recovers the classical notion of surface tension in the limit. We provide some regularity results and the determination of the contact angle, supplied with various asymptotics.

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  1. The weighted isoperimetric inequality and Sobolev inequality outside convex sets

    math.AP 2025-10 reject novelty 3.0 of 10

    The paper's main isoperimetric and Sobolev claims rest on a weight assumption that is impossible as written, so the outside-convex-set theorems are vacuous.

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