We prove a convexity property of the surface tension corresponding to a nonlocal, anisotropic free-energy functional of van der Waals type which implies that the Wulff shape is strictly convex and smooth. We also prove that the transport coefficients of the limiting anisotropic motion by mean curvature obtained in [33] are strictly positive and equal to the stiffness parameters determined by the surface tension.
Bellettini, G., Butta', P., Presutti, E. (2001). Sharp interface limits of non local anisotropic interactions. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 159(2), 109-135 [10.1007/s002050100149].
Sharp interface limits of non local anisotropic interactions
BELLETTINI, GIOVANNI;
2001-01-01
Abstract
We prove a convexity property of the surface tension corresponding to a nonlocal, anisotropic free-energy functional of van der Waals type which implies that the Wulff shape is strictly convex and smooth. We also prove that the transport coefficients of the limiting anisotropic motion by mean curvature obtained in [33] are strictly positive and equal to the stiffness parameters determined by the surface tension.
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https://hdl.handle.net/11365/1017486