Consistency of the Flat Flow Solution to the Volume Preserving Mean Curvature Flow
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Consistency of the Flat Flow Solution to the Volume Preserving Mean Curvature Flow
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Archive for Rational Mechanics and Analysis
ISSN
0003-9527
e-ISSN
1432-0673
Volume of the periodical
248
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
58
Pages from-to
1
UT code for WoS article
001117814000001
EID of the result in the Scopus database
2-s2.0-85178911021