A1 Journal article (refereed)
Stationary sets of the mean curvature flow with a forcing term (2021)


Julin, V., & Niinikoski, J. (2021). Stationary sets of the mean curvature flow with a forcing term. Advances in Calculus of Variations, Ahead of Print. https://doi.org/10.1515/acv-2021-0019


JYU authors or editors


Publication details

All authors or editors: Julin, Vesa; Niinikoski, Joonas

Journal or series: Advances in Calculus of Variations

ISSN: 1864-8258

eISSN: 1864-8266

Publication year: 2021

Publication date: 08/08/2021

Volume: Ahead of Print

Publisher: Walter de Gruyter GmbH

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1515/acv-2021-0019

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/77405

Publication is parallel published: https://arxiv.org/abs/2011.13666


Abstract

We consider the flat flow solution to the mean curvature equation with forcing in ℝn. Our main resultstates that tangential balls in ℝn under a flat flow with a bounded forcing term will experience fattening, which generalizes the result in [N. Fusco, V. Julin and M. Morini, Stationary sets and asymptotic behavior ofthe mean curvature flow with forcing in the plane, preprint (2020), https://arxiv.org/abs/2004.07734] from the planar case to higher dimensions. Then, as in the planar case, we characterize stationary sets in ℝn for a constant forcing term as finite unions of equisize balls with mutually positive distance.


Keywords: partial differential equations; calculus of variations

Free keywords: forced mean curvature flow; stationary sets; critical sets


Contributing organizations


Ministry reporting: No, publication in press

Preliminary JUFO rating: 1


Last updated on 2022-20-09 at 13:54