Stripe patterns and the eikonal equation

M.A. Peletier, M. Veneroni

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Samenvatting

We study a new formulation for the eikonal equation |¿u| = 1 on a bounded subset of R2. Considering a field P of orthogonal projections onto 1-dimensional subspaces, with div P ¿ L2, we prove existence and uniqueness for solutions of the equation P div P = 0. We give a geometric description, comparable with the classical case, and we prove that such solutions exist only if the domain is a tubular neighbourhood of a regular closed curve. This formulation provides a useful approach to the analysis of stripe patterns. It is specifically suited to systems where the physical properties of the pattern are invariant under rotation over 180 degrees, such as systems of block copolymers or liquid crystals.
Originele taal-2Engels
UitgeverijarXiv.org
Aantal pagina's9
StatusGepubliceerd - 2009

Publicatie series

NaamarXiv.org [math.AP]
Volume0904.0731

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