English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we propose a new scheme for anisotropic motion by meancurvature in $\R^d$. The scheme consists of a phase-field approximation of themotion, where the nonlinear diffusive terms in the corresponding anisotropicAllen-Cahn equation are linearized in the Fourier space. In real space, thiscorresponds to the convolution with a kernel of the form \[ K_{\phi,t}(x) =\F^{-1}\left[ e^{-4\pi^2 t \phi^o(\xi)} \right](x). \] We analyse the resultingscheme, following the work of Ishii-Pires-Souganidis on the convergence of theBence-Merriman-Osher algorithm for isotropic motion by mean curvature. The maindifficulty here, is that the kernel $K_{\phi,t}$ is not positive and that itsmoments of order 2 are not in $L^1(\R^d)$. Still, we can show that in one sensethe scheme is consistent with the anisotropic mean curvature flow.

Consistency result for a non monotone scheme for anisotropic mean curvature flow