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Hokkaido University Preprint Series in Mathematics >
A rigorous setting for the reinitialization of first order level set equations
| Title: | A rigorous setting for the reinitialization of first order level set equations |
| Authors: | HAMAMUKI, NAO Browse this author | | NTOVORIS, Eleftherios Browse this author |
| Issue Date: | 23-Jun-2015 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1074 |
| Start Page: | 1 |
| End Page: | 45 |
| Abstract: | In this paper we set up a rigorous justification for the reinitialization algorithm. Using the theory of viscosity solutions, we propose a well-posed Hamilton-Jacobi equation with a parameter, which is derived from homogenization for a Hamiltonian discontinuous in time which appears in the reinitialization. We prove that, as the parameter tends to infinity, the solution of the initial value problem converges to a signed distance function to the evolving interfaces. A locally uniform convergence is shown when the distance function is continuous, whereas a weaker notion of convergence is introduced to establish a convergence result to a possibly discontinuous distance function. In terms of the geometry of the interfaces, we give a necessary and sufficient condition for the continuity of the distance function. We also propose another simpler equation whose solution has a gradient bound away from zero. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69878 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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