160 citations · 192 across the 13 of their papers we have counts for
19 papers
Two-phase almost minimizers for a fractional free boundary problem
Mark Allen, Mariana Smit Vega Garcia
In this paper, we study almost minimizers to a fractional Alt-Caffarelli-Friedman type functional. Our main results concern the optimal regularity of almost minimizers as…
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…
Sharp quantitative Faber-Krahn inequalities and the Alt-Caffarelli-Friedman monotonicity formula
Mark Allen, Dennis Kriventsov, Robin Neumayer
The objective of this paper is two-fold. First, we establish new sharp quantitative estimates for Faber-Krahn inequalities on simply connected space forms. We prove that the gap be…
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…