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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We propose a level-set method for a mean curvature flow whose boundary isprescribed by interpreting the boundary as an obstacle. Since the correspondingobstacle problem is globally solvable, our method gives a global-in-timelevel-set mean curvature flow under a prescribed boundary with no restrictionof the profile of an initial hypersurface. We show that our solution agreeswith a classical mean curvature flow under the Dirichlet condition. We moreoverprove that our solution agrees with a level-set flow under the Dirichletcondition constructed by P. Sternberg and W. P. Ziemer (1994), where theinitial hypersurface is contained in a strictly mean-convex domain and theprescribed boundary is on the boundary of the domain.

A level-set method for a mean curvature flow with a prescribed boundary