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- W3093238748 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. MSC 2010: 35D40; 35F25; 35A35" @default.
- W3093238748 created "2020-10-22" @default.
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- W3093238748 date "2015-06-23" @default.
- W3093238748 modified "2023-09-23" @default.
- W3093238748 title "A rigorous setting for the reinitialization of first order level set equations" @default.
- W3093238748 hasPublicationYear "2015" @default.
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