The existence of a weak solution to volume preserving mean curvature flow in higher dimensions

DOI10.1007/s00205-023-01881-warXiv2201.10850OpenAlexW4377012284MaRDI QIDQ6040849

Keisuke Takasao

Publication date: 22 May 2023

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.10850

zbMATH Keywords

Allen-Cahn equation with nonlocal termdistributional BV-solutionfamily of integral varifolds

Mathematics Subject Classification ID

Weak solutions to PDEs (35D30) Quasilinear parabolic equations with mean curvature operator (35K93) Flows related to mean curvature (53E10)

Related Items

Weak-strong uniqueness for volume-preserving mean curvature flow

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence and regularity of mean curvature flow with transport term in higher dimensions
• Global solutions to the volume-preserving mean-curvature flow
• Convergence of the thresholding scheme for multi-phase mean-curvature flow
• Stability of spheres under volume-preserving mean curvature flow
• Mass conserving Allen-Cahn equation and volume preserving mean curvature flow
• Asymptotic behavior for singularities of the mean curvature flow
• The Allen-Cahn action functional in higher dimensions
• The volume-preserving mean curvature flow in Euclidean space
• Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
• Shape analysis via oriented distance functions
• Implicit time discretization for the mean curvature flow equation
• Volume-preserving mean curvature flow of rotationally symmetric surfaces
• Gradient-flow techniques for the analysis of numerical schemes for multi-phase mean-curvature flow
• Integrality of varifolds in the singular limit of reaction-diffusion equations
• Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory.
• Volume preserving mean curvature flow for star-shaped sets
• An existence theorem for Brakke flow with fixed boundary conditions
• Convergence of thresholding schemes incorporating bulk effects
• The sharp quantitative isoperimetric inequality
• Convergence of the Allen-Cahn equation with constraint to Brakke's mean curvature flow
• On a modified conjecture of De Giorgi
• Allen-Cahn approximation of mean curvature flow in Riemannian manifolds I, uniform estimates
• Allen–Cahn approximation of mean curvature flow in Riemannian manifolds, II: Brakke's flows
• A modified phase field approximation for mean curvature flow with conservation of the volume
• Existence of weak solution for volume preserving mean curvature flow via phase field method
• The volume preserving mean curvature flow.
• Nonlocal reaction—diffusion equations and nucleation
• The Motion of a Surface by Its Mean Curvature. (MN-20)
• The volume preserving mean curvature flow near spheres
• Volume-Preserving Mean Curvature Flow as a Limit of a Nonlocal Ginzburg-Landau Equation
• The volume-preserving motion by mean curvature as an asymptotic limit of reaction-diffusion equations
• Convergence of the Allen‐Cahn Equation to Multiphase Mean Curvature Flow
• Brakke's Mean Curvature Flow
• Curvature-Driven Flows: A Variational Approach
• On Obstacle Problem for Brakke's Mean Curvature Flow
• Convergence of the Allen--Cahn Equation with Neumann Boundary Conditions
• On the existence of mean curvature flow with transport term

This page was built for publication: The existence of a weak solution to volume preserving mean curvature flow in higher dimensions