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Anisotropic mean curvature on facets and relations with capillarity

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Języki publikacji
EN
Abstrakty
EN
Given an anisotropy ɸ on R3, we discuss the relations between the ɸ-calibrability of a facet F ⊂ ∂E of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet ̃︀ BFɸ of the unit ball of ɸ, ɸ-calibrability is equivalent to show the existence of a ɸ-subunitary vector field in F, with suitable normal trace on @F, and with constant divergence equal to the ɸ-mean curvature of F. Assuming E convex at F, ̃︀ BFɸ a disk, and F (strictly) ɸ-calibrable, such a vector field is obtained by solving the capillary problem on F in absence of gravity and with zero contact angle. We show some examples of facets for which it is possible, even without the strict ɸ-calibrability assumption, to build one of these vector fields. The construction provides, at least for convex facets of class C1,1, the solution of the total variation flow starting at 1F.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
1
Numer
1
Opis fizyczny
Daty
otrzymano
2015-02-19
zaakceptowano
2015-06-15
online
2015-09-04
Twórcy
  • S.I.S.S.A., via Bonomea 265, 34136, Trieste, Italy
  • Dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca
    Scientifica 1, 00133 Roma, Italy
  • INFN Laboratori Nazionali di Frascati (LNF), via E. Fermi 40, Frascati 00044 Roma, Italy
autor
  • S.I.S.S.A., via Bonomea 265, 34136, Trieste, Italy
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_1515_geofl-2015-0005
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