Nonlocal capillarity for anisotropic kernels

We study a nonlocal capillarity problem with interaction kernels that are possibly anisotropic and not necessarily invariant under scaling. In particular, the lack of scale invariance will be modeled via two different fractional exponents  s 1 , s 2 ∈ ( 0 , 1 ) which take into account the possibilit...

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Bibliographic Details
Published in:Mathematische annalen 2024-04, Vol.388 (4), p.3785-3846
Main Authors: De Luca, Alessandra, Dipierro, Serena, Valdinoci, Enrico
Format: Article
Language:English
Subjects:
Capillarity
Contact angle
Mathematics
Mathematics and Statistics
Particle interactions
Scale invariance
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Summary:We study a nonlocal capillarity problem with interaction kernels that are possibly anisotropic and not necessarily invariant under scaling. In particular, the lack of scale invariance will be modeled via two different fractional exponents  s 1 , s 2 ∈ ( 0 , 1 ) which take into account the possibility that the container and the environment present different features with respect to particle interactions. We determine a nonlocal Young’s law for the contact angle and discuss the unique solvability of the corresponding equation in terms of the interaction kernels and of the relative adhesion coefficient.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-023-02623-9