Consistency of the Flat Flow Solution to the Volume Preserving Mean Curvature Flow

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10476934" target="_blank" >RIV/00216208:11320/24:10476934 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Q9-n3itrf0" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Q9-n3itrf0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00205-023-01944-y" target="_blank" >10.1007/s00205-023-01944-y</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Consistency of the Flat Flow Solution to the Volume Preserving Mean Curvature Flow

Popis výsledku v původním jazyce

We consider the flat flowsolution, obtained via a discreteminimizingmovement scheme, to the volume preserving mean curvature flow starting from C(1,)1-regular set. We prove the consistency principle, which states that (any) flat flow solution agrees with the classical solution as long as the latter exists. In particular the flat flow solution is unique and smooth up to the first singular time. We obtain the result by proving the full regularity for the discrete time approximation of the flat flow such that the regularity estimates are stable with respect to the time discretization. Our method can also be applied in the case of the mean curvature flow and thus it provides an alternative proof, not relying on comparison principle, for the consistency between the flat flow solution and the classical solution for C-1,C-1-regular initial sets.

Název v anglickém jazyce

Consistency of the Flat Flow Solution to the Volume Preserving Mean Curvature Flow

Popis výsledku anglicky

We consider the flat flowsolution, obtained via a discreteminimizingmovement scheme, to the volume preserving mean curvature flow starting from C(1,)1-regular set. We prove the consistency principle, which states that (any) flat flow solution agrees with the classical solution as long as the latter exists. In particular the flat flow solution is unique and smooth up to the first singular time. We obtain the result by proving the full regularity for the discrete time approximation of the flat flow such that the regularity estimates are stable with respect to the time discretization. Our method can also be applied in the case of the mean curvature flow and thus it provides an alternative proof, not relying on comparison principle, for the consistency between the flat flow solution and the classical solution for C-1,C-1-regular initial sets.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Archive for Rational Mechanics and Analysis

ISSN

0003-9527

e-ISSN

1432-0673

Svazek periodika

248

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

58

Strana od-do

1

Kód UT WoS článku

001117814000001

EID výsledku v databázi Scopus

2-s2.0-85178911021