We prove that for any H : R(2) -> R which is Z(2)-periodic, there exists H(epsilon), which is smooth, epsilon-close to H in L(1), with L(infinity)-norm controlled by the one of H, and with the same average of H, for which there exists a smooth closed curve gamma(epsilon) whose curvature is H(epsilon). 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.
Closed curves of prescribed curvature and a pinning effect / M. Novaga, E. Valdinoci. - In: NETWORKS AND HETEROGENEOUS MEDIA. - ISSN 1556-1801. - 6:1(2011), pp. 77-88. [10.3934/nhm.2011.6.77]
Closed curves of prescribed curvature and a pinning effect
E. ValdinociUltimo
2011
Abstract
We prove that for any H : R(2) -> R which is Z(2)-periodic, there exists H(epsilon), which is smooth, epsilon-close to H in L(1), with L(infinity)-norm controlled by the one of H, and with the same average of H, for which there exists a smooth closed curve gamma(epsilon) whose curvature is H(epsilon). 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.File | Dimensione | Formato | |
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