Closed curves of prescribed curvature and a pinning effect

Matteo Novaga, Enrico Valdinoci

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We prove that for any H : R{double-struck}2 → R{double-struck} which is Z{double-struck}2-periodic, there exists H, which is smooth, ε-close to H in L1, with L-norm controlled by the one of H, and with the same average of H, for which there exists a smooth closed curve γ whose curvature is H. A pinning phenomenon for curvature driven flow with a periodic forcing term then follows. Namely, curves in fine periodic media may be moved only by small amounts, of the order of the period.

Original languageEnglish
Pages (from-to)77-88
Number of pages12
JournalNetworks and Heterogeneous Media
Volume6
Issue number1
DOIs
Publication statusPublished - 1 Mar 2011
Externally publishedYes

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