TY - JOUR
T1 - Closed curves of prescribed curvature and a pinning effect
AU - Novaga, Matteo
AU - Valdinoci, Enrico
PY - 2011/3/1
Y1 - 2011/3/1
N2 - 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.
AB - 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.
KW - Heterogeneous media
KW - Pinning phenomena
KW - Prescribed curvature
UR - http://www.scopus.com/inward/record.url?scp=79954527814&partnerID=8YFLogxK
U2 - 10.3934/nhm.2011.6.77
DO - 10.3934/nhm.2011.6.77
M3 - Article
AN - SCOPUS:79954527814
SN - 1556-1801
VL - 6
SP - 77
EP - 88
JO - Networks and Heterogeneous Media
JF - Networks and Heterogeneous Media
IS - 1
ER -