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math.AP2018
Full and partial regularity for a class of nonlinear free boundary problems
Aram Karakhanyan
In this paper we classify the nonnegative global minimizers of the functional \[ J_F(u)=\int_ΩF(|\nabla u|^2)+λ^2χ_{\{u>0\}}, \] where satisfies some structural conditions and…
math.AP2018
Refractor surfaces determined by near-field data
Aram Karakhanyan, Ahmad Sabra
In this paper we study the near-field refractor problem with point source at the origin and prescribed target on the given receiver surface . This nonvariational problem can be…
math.AP2018
A free boundary problem driven by the biharmonic operator
Serena Dipierro, Aram Karakhanyan, Enrico Valdinoci
In this paper we consider the minimization of the functional \[ J[u]:=\int_Ω|Δu|^2+χ_{\{u>0\}} \] in the admissible class of functions \[ \mathcal A:= \left\{u\in W^{2, 2}(Ω) {\mbo…