3 citations · 11 across the 30 of their papers we have counts for
5 papers · 2 filters
A remark on an obstacle problem with lower regularity
Aram Karakhanyan
We construct a monotone quantity for the classical obstacle problem with non-smooth obstacle, and show that the blow-ups are homogeneous functions of degree .
Regularity for the two phase singular perturbation problems
Aram Karakhanyan
We prove that an a priori BMO gradient estimate for the two phase singular perturbation problem implies Lipschitz regularity for the limits. This problem arises in the mathematical…
Structure of singularities in the nonlinear nerve conduction problem
Aram Karakhanyan
We give a characterisation of the singular points of the free boundary for viscosity solutions of the nonlinear equation \begin{equation}F(D^2 u)=-χ_{\{u>0\}},\t…
A nonlocal free boundary problem with Wasserstein distance
Aram Karakhanyan
We study the probability measures minimizing the functional \[ J[ρ]=\iint \log\frac1{|x-y|}dρ(x)dρ(y)+d^2(ρ, ρ_0), \] where is a given probabil…
Limit behaviour of a singular perturbation problem for the biharmonic operator
Serena Dipierro, Aram L. Karakhanyan, Enrico Valdinoci
We study here a singular perturbation problem of biLaplacian type, which can be seen as the biharmonic counterpart of classical combustion models. We provide different results, tha…