124 citations · 1.4k across the 62 of their papers we have counts for
15 papers · 1 filter
Smoothness up to the free boundary for the -Laplacian evolution equation and the -Gauss curvature flow
Albert Chau, Ben Weinkove
The -Laplacian evolution equation and the -Gauss curvature flow with a flat side are degenerate parabolic equations with evolving free boundaries. We give proofs of smooth sh…
Smooth solutions of degenerate linear parabolic equations and the porous medium equation
Albert Chau, Ben Weinkove
We prove existence of smooth solutions to linear degenerate parabolic equations on bounded domains assuming a structure condition of Fichera. We use this to give a proof of a smoot…
The perfect conductivity problem with arbitrary vanishing orders and non-trivial topology
Morgan Sherman, Ben Weinkove
The perfect conductivity problem concerns optimal bounds for the magnitude of an electric field in the presence of almost touching perfect conductors. This reduces to obtaining gra…
Instantaneous convexity breaking for the quasi-static droplet model
Albert Chau, Ben Weinkove
We consider a well-known quasi-static model for the shape of a liquid droplet. The solution can be described in terms of time-evolving domains in . We give an example…
Concavity of solutions to semilinear equations in dimension two
Albert Chau, Ben Weinkove
We consider the Dirichlet problem for a class of semilinear equations on two dimensional convex domains. We give a sufficient condition for the solution to be concave. Our conditio…
The insulated conductivity problem, effective gradient estimates and the maximum principle
Ben Weinkove
We consider the insulated conductivity problem with two unit balls as insulating inclusions, a distance of order apart. The solution represents the electric poten…