1 citations · 2 across the 2 of their papers we have counts for
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Rectifiability and uniqueness of blow-ups for points with positive Alt-Caffarelli-Friedman limit
Mark Allen, Dennis Kriventsov, Robin Neumayer
We study the regularity of the interface between the disjoint supports of a pair of nonnegative subharmonic functions. The portion of the interface where the Alt-Caffarelli-Friedma…
Minimizers of a free boundary problem on three-dimensional cones
Mark Allen, Blake Barker, Jason Gardiner +1
We consider a free boundary problem on three-dimensional cones depending on a parameter c and study when the free boundary is allowed to pass through the vertex of the cone. Combin…
The Inhomogeneous Boundary Harnack Principle for Fully Nonlinear and p-Laplace equations
Mark Allen, Dennis Kriventsov, Henrik Shahgholian
We prove a boundary Harnack principle in Lipschitz domains with small constant for fully nonlinear and -Laplace type equations with a right hand side, as well as for the Laplace…
A new boundary Harnack principle (equations with right hand side)
Mark Allen, Henrik Shahgholian
We introduce a new boundary Harnack principle in Lipschitz domains for equations with right hand side. Our approach, which uses comparisons and blow-ups, will adapt to more general…
The fractional unstable obstacle problem
Mark Allen, Mariana Smit Vega Garcia
We study a model for combustion on a boundary. Specifically, we study certain generalized solutions of the equation \[ (-Δ)^s u = χ_{\{u>c\}} \] for and an arbitrary consta…
Uniqueness for weak solutions of parabolic equations with a fractional time derivative
Mark Allen
We prove uniqueness for weak solutions to abstract parabolic equations with the fractional Marchaud or Caputo time derivative. We consider weak solutions in time for divergence for…