Geodesic
Curve shortening flow in heterogeneous media
Annalisa Cesaroni1 ; Matteo Novaga2 orcid ; Enrico Valdinoci3 orcid
1Università di Padova, Italy
2Università di Pisa, Italy
3Università degli Studi di Milano, Italy
Interfaces and free boundaries, Tome 13 (2011) no. 4, pp. 485-505

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DOI

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 L∞-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.
DOI : 10.4171/ifb/269
Classification : 00-XX

Annalisa Cesaroni  1   ; Matteo Novaga  2   ; Enrico Valdinoci  3

1 Università di Padova, Italy
2 Università di Pisa, Italy
3 Università degli Studi di Milano, Italy 
Annalisa Cesaroni; Matteo Novaga; Enrico Valdinoci. Curve shortening flow in heterogeneous media. Interfaces and free boundaries, Tome 13 (2011) no. 4, pp. 485-505. doi: 10.4171/ifb/269
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