Abstract
We investigate the stability of the evolution by anysotropic and crystalline curvature starting from an initial surface equal to the Wulff shape. It is well known that the Wulff shape evolves selfsimilarly according to the law V = -k ø n ø .Here the index ø refers to the underlying anisotropy described by the Wulff shape, so that k ø is the relative mean curvature and n ø is the Cahn-Hoffmann conormal vector field. Such selfsimilar evolution is also known to be stable under small perturbations of the initial surface in the isotropic setting (the Wulff shape is a sphere) or in 2D if the underlying anisotropy is symmetric. We show that this evolution is unstable for some specific choices of the Wulff shape both rotationally symmetric and fully crystalline.
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Paolini, M., Pasquarelli, F. (2002). Unstable Crystalline Wulff Shapes in 3D. In: dal Maso, G., Tomarelli, F. (eds) Variational Methods for Discontinuous Structures. Progress in Nonlinear Differential Equations and Their Applications, vol 51. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8193-7_10
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DOI: https://doi.org/10.1007/978-3-0348-8193-7_10
Publisher Name: Birkhäuser, Basel
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