Mean curvature flow with triple junctions in higher space dimensions

DOI10.1007/s00205-013-0668-yzbMath1291.53078arXiv1207.2351OpenAlexW2073758588MaRDI QIDQ2436328

Yoshihito Kohsaka, Daniel Depner, Harald Garcke

Publication date: 24 February 2014

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

Full work available at URL: https://arxiv.org/abs/1207.2351

zbMATH Keywords

mean curvature flowtriple junctionsshort time existenceparabolic Hölder spaceshypersurfaces in Euclidean spacessurfaces with boundary clusters

Mathematics Subject Classification ID

Related Items (13)

Minimizing Movements for Mean Curvature Flow of Partitions ⋮ Minimizing movements for mean curvature flow of droplets with prescribed contact angle ⋮ Curvature estimates for stable minimal surfaces with a common free boundary ⋮ Weak-strong uniqueness for the mean curvature flow of double bubbles ⋮ On the existence of canonical multi-phase Brakke flows ⋮ On convergence of solutions to equilibria for fully nonlinear parabolic systems with nonlinear boundary conditions ⋮ Non-linear stability of double bubbles under surface diffusion ⋮ On the surface diffusion flow with triple junctions in higher space dimensions ⋮ On a degenerate parabolic system describing the mean curvature flow of rotationally symmetric closed surfaces ⋮ A local regularity theorem for mean curvature flow with triple edges ⋮ Long time existence of solutions to an elastic flow of networks ⋮ Minimizing movements for forced anisotropic mean curvature flow of partitions with mobilities ⋮ Existence of a lens-shaped cluster of surfaces self-shrinking by mean curvature

Cites Work

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• Lecture notes on mean curvature flow
• Mean curvature motion of graphs with constant contact angle at a free boundary
• Flow by mean curvature of convex surfaces into spheres
• Stable and unstable manifolds for quasilinear parabolic systems with fully nonlinear boundary conditions
• Nonlinear stability of stationary solutions for curvature flow with triple junction
• The heat equation shrinking convex plane curves
• The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
• Non-parametric mean curvature evolution with boundary conditions
• On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation
• Parabolic boundary value problems
• Classical solutions for Hele-Shaw models with surface tension
• Regularity theory for mean curvature flow
• Elliptic partial differential equations of second order
• Regularity estimates for solutions to the mean curvature flow with a Neumann boundary condition
• Linearized stability analysis of surface diffusion for hypersurfaces with triple lines
• Evolution of convex lens-shaped networks under the curve shortening flow
• Mean Curvature Motion of Triple Junctions of Graphs in Two Dimensions
• The Motion of a Surface by Its Mean Curvature. (MN-20)
• Smooth solutions to a class of free boundary parabolic problems
• EVOLUTION OF GRAIN BOUNDARIES
• Curvature evolution of nonconvex lens-shaped domains
• Surfactant Spreading on Thin Viscous Films: Nonnegative Solutions of A Coupled Degenerate System
• Analytic semigroups and optimal regularity in parabolic problems
• Parametric approximation of surface clusters driven by isotropic and anisotropic surface energies

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