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math.AP2020
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…
math.AP2020
Optimal regularity for a two-phase obstacle-like problem with logarithmic singularity
Dennis Kriventsov, Henrik Shahgholian
We consider the semilinear problem \[ Δu = λ_+ \left(-\log u^+\right) 1_{\{u > 0\}} - λ_- \left(-\log u^- \right) 1_{\{u < 0\}} \qquad \hbox{ in } B_1, \] where is the unit b…