Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
839192 | Nonlinear Analysis: Theory, Methods & Applications | 2016 | 19 Pages |
Abstract
We introduce a notion of solution to the 1-harmonic flow–i.e., the formal gradient flow of the total variation with respect to the L2L2-distance–from a domain of RmRm into a connected subset of the image of a smooth Jordan curve. For such notion, we establish existence and uniqueness of solutions to the homogeneous Neumann problem. We also discuss a consistent notion of solution when the target space is a smooth (n−1)(n−1)-dimensional manifold whose geodesics are unique, presenting conjectures and open questions related to it.
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Authors
Agnese Di Castro, Lorenzo Giacomelli,