6533b855fe1ef96bd12afddc

RESEARCH PRODUCT

Stationary sets of the mean curvature flow with a forcing term

Vesa JulinJoonas Niinikoski

subject

osittaisdifferentiaaliyhtälötMean curvature flowForcing (recursion theory)Mean curvatureEuclidean spaceApplied Mathematics010102 general mathematicsMathematical analysisstationary setscritical setsvariaatiolaskenta01 natural sciences35J93Term (time)010101 applied mathematicsMathematics - Analysis of PDEsFlow (mathematics)forced mean curvature flowBounded functionFOS: Mathematics0101 mathematicsConstant (mathematics)AnalysisAnalysis of PDEs (math.AP)Mathematics

description

We consider the flat flow approach for the mean curvature equation with forcing in an Euclidean space $\mathbb R^n$ of dimension at least 2. Our main results states that tangential balls in $\mathbb R^n$ under any flat flow with a bounded forcing term will experience fattening, which generalizes the result by Fusco, Julin and Morini from the planar case to higher dimensions. Then, as in the planar case, we are able to characterize stationary sets in $\mathbb R^n$ for a constant forcing term as finite unions of equisized balls with mutually positive distance.

yearjournalcountryeditionlanguage
2020-11-27Advances in Calculus of Variations
https://doi.org/10.1515/acv-2021-0019