On Obstacle Problem for Brakke's Mean Curvature Flow

DOI10.1137/21M1400432zbMath1479.35547arXiv2102.06375OpenAlexW3212344773MaRDI QIDQ5014287

Keisuke Takasao

Publication date: 1 December 2021

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.06375

zbMATH Keywords

Allen-Cahn equationphase-field methodsubsolutions and supersolution

Mathematics Subject Classification ID

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

Related Items (1)

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

Cites Work

• 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
• Mean curvature flow with obstacles
• Motion of level sets by mean curvature. I
• A local regularity theorem for mean curvature flow
• Boundary Harnack principle for \(p\)-harmonic functions in smooth Euclidean domains
• Mean curvature flow with obstacles: existence, uniqueness and regularity of solutions
• The Allen-Cahn action functional in higher dimensions
• Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
• Generation and propagation of interfaces for reaction-diffusion equations
• The obstacle problem revisited
• Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
• Implicit time discretization for the mean curvature flow equation
• On the mean curvature flow of grain boundaries
• Remarks on viscosity solutions for mean curvature flow with obstacles
• Integrality of varifolds in the singular limit of reaction-diffusion equations
• Convergence of the phase-field equations to the Mullins-Sekerka problem with kinetic undercooling
• On obstacle problem for mean curvature flow with driving force
• A general regularity theory for weak mean curvature flow
• Existence of weak solution for mean curvature flow with transport term and forcing term
• On an evolution equation in a cell motility model
• On a modified conjecture of De Giorgi
• On the first variation of a varifold
• Phase field method for mean curvature flow with boundary constraints
• Convergence of perturbed Allen-Cahn equations to forced mean curvature flow
• Existence of weak solution for volume preserving mean curvature flow via phase field method
• Regularity of the obstacle problem for a fractional power of the laplace operator
• A simple proof of convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
• Phase transitions and generalized motion by mean curvature
• The Motion of a Surface by Its Mean Curvature. (MN-20)
• Elliptic regularization and partial regularity for motion by mean curvature
• Brakke's Mean Curvature Flow
• Curvature-Driven Flows: A Variational Approach
• A second derivative Hölder estimate for weak mean curvature flow
• Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
• On the existence of mean curvature flow with transport term

This page was built for publication: On Obstacle Problem for Brakke's Mean Curvature Flow