Approximation rates for regularized level set power mean curvature flow

被引：4

作者：

Kroener, Heiko ^{[1
]}

机构：

[1] Univ Hamburg, Fachbereich Math, Bundesstr 55, D-20146 Hamburg, Germany

来源：

PORTUGALIAE MATHEMATICA | 2017年 / 74卷 / 02期

关键词：

Geometric evolution equation; level set mean curvature flow; regularization; rates of convergence; EQUATIONS; EVOLUTION;

D O I：

10.4171/PM/1995

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In [11] the evolution of hypersurfaces in Rn+1 with normal speed equal to a power k > 1 of the mean curvature is considered and the level set solution u of the flow is obtained as the C-0-limit of a sequence u(epsilon) of smooth functions solving the regularized level set equations. We prove a rate for this convergence.

引用

页码：115 / 126

页数：12

共 50 条

[1] Study of a finite volume scheme for the regularized mean curvature flow level set equation
Eymard, Robert
Handlovicova, Angela
Mikula, Karol
IMA JOURNAL OF NUMERICAL ANALYSIS, 2011, 31 (03) : 813 - 846
[2] A LEVEL SET CRYSTALLINE MEAN CURVATURE FLOW OF SURFACES
Giga, Yoshikazu
Pozar, Norbert
ADVANCES IN DIFFERENTIAL EQUATIONS, 2016, 21 (7-8) : 631 - 698
[3] FINITE ELEMENT APPROXIMATION OF LEVEL SET MOTION BY POWERS OF THE MEAN CURVATURE
Kroner, Axel
Kroener, Eva
Kroener, Heiko
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2018, 40 (06): : A4158 - A4183
[4] Numerical approximation of mean curvature flow of graphs and level sets
Deckelnick, K
Dziuk, G
MATHEMATICAL ASPECTS OF EVOLVING INTERFACES, 2003, 1812 : 53 - 87
[5] Level set approach to mean curvature flow in arbitrary codimension
Ambrosio, L
Soner, HM
JOURNAL OF DIFFERENTIAL GEOMETRY, 1996, 43 (04) : 693 - 737
[6] Level set mean curvature flow with Neumann boundary conditions
Aimi, Satoru
HOKKAIDO MATHEMATICAL JOURNAL, 2023, 52 (01) : 41 - 64
[7] On level set formulations for anisotropic mean curvature flow and surface diffusion
Clarenz, U
Hausser, F
Rumpf, M
Voigt, A
Weikard, U
MULTISCALE MODELING IN EPITAXIAL GROWTH, 2005, 149 : 227 - 237
[8] A LEVEL-SET METHOD FOR A MEAN CURVATURE FLOW WITH A PRESCRIBED BOUNDARY
Bian, Xingzhi
Giga, Yoshikazu
Mitake, Hiroyoshi
ADVANCES IN DIFFERENTIAL EQUATIONS, 2025, 30 (1-2) : 1 - 34
[9] Approximation of the anisotropic mean curvature flow
Chambolle, Antonin
Novaga, Matteo
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2007, 17 (06): : 833 - 844
[10] Regularity and stability results for the level set flow via the mean curvature flow with surgery
Mramor, Alexander
COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2021, 29 (08) : 1783 - 1811

← 1 2 3 4 5 →