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math.AP2018
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…
math.AP2018
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…