7 citations · 13 across the 12 of their papers we have counts for
8 papers · 1 filter
Rigidity and stability for the Bogovskii constant
Glen Wheeler
We prove that balls are the unique minimisers of the Bogovskii constant among bounded connected Lipschitz domains in , , resolving Open Problem 2 of Gazzola,…
Concentration-compactness for the geometric polyharmonic heat flow
James McCoy, Scott Parkins, Glen Wheeler +1
We develop a concentration-compactness theory for geometric evolution equations of arbitrarily high order, using the geometric polyharmonic heat flow of closed immersed surfaces in…
Convergence of solutions to a convective Cahn-Hilliard type equation of the sixth order in case of small deposition rates
Piotr Rybka, Glen Wheeler
We show stabilisation of solutions to the sixth-order convective Cahn-Hilliard equation. {The problem} has the structure of a gradient flow perturbed by a quadratic destabilising t…
The -elastic flow for planar closed curves with constant parametrization
Shinya Okabe, Glen Wheeler
In this paper, we consider the -gradient flow for the modified -elastic energy defined on planar closed curves. We formulate a notion of weak solution for the flow and prov…
The length-constrained ideal curve flow
James McCoy, Glen Wheeler, Yuhan Wu
A recent article by the first two authors together with B Andrews and V-M Wheeler considered the so-called `ideal curve flow', a sixth order curvature flow that seeks to deform clo…
Higher order curvature flows of plane curves with generalised Neumann boundary conditions
James McCoy, Glen Wheeler, Yuhan Wu
We consider the parabolic polyharmonic diffusion and -gradient flows of the -th arclength derivative of curvature for regular closed curves evolving with generalised Neuman…