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A rigorous setting for the reinitialization of first order level set equations

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84218

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
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

Submitter: 数学紀要登録作業用

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