JournalsifbVol. 13, No. 4pp. 485–505

Curve shortening flow in heterogeneous media

  • Annalisa Cesaroni

    Università di Padova, Italy
  • Matteo Novaga

    Università di Pisa, Italy
  • Enrico Valdinoci

    Università degli Studi di Milano, Italy
Curve shortening flow in heterogeneous media cover
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Abstract

In recent years, there has been a growing interest in geometric evolutions in heterogeneous media. Here we consider curvature driven flows of planar curves with an additional space-dependent forcing term, and we look for estimates which depend only on the LL^\infty-norm of the forcing term. Our motivation comes from a homogenization problem, which we can rigorously solve in the special case when the initial curve is a graph and the forcing term does not depend on the vertical direction. In such case, we are also able to define a solution of the evolution even if the forcing term is just a bounded function, not necessarily continuous.

Cite this article

Annalisa Cesaroni, Matteo Novaga, Enrico Valdinoci, Curve shortening flow in heterogeneous media. Interfaces Free Bound. 13 (2011), no. 4, pp. 485–505

DOI 10.4171/IFB/269