TY - JOUR
T1 - Anisotropic mean curvature on facets and relations with capillarity
Y1 - 2015
A1 - Stefano Amato
A1 - Lucia Tealdi
A1 - Giovanni Bellettini
AB - We discuss the relations between the anisotropic calibrability of a facet F of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet of the Wulff shape, calibrability is equivalent to show the existence of an anisotropic subunitary vector field in $F, with suitable normal trace on the boundary of the facet, and with constant divergence equal to the anisotropic mean curvature of F. When the Wulff shape is a cylynder, assuming E convex at F, and F (strictly) 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 calibrability assumption, to build one of these vector fields. The construction provides, at least for convex facets of class C^{1,1}, the solution of the total variation flow starting at 1_F.
PB - de Gruyter
UR - http://urania.sissa.it/xmlui/handle/1963/34481
U1 - 34663
U2 - Mathematics
U4 - 1
U5 - MAT/05
ER -