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math.AP2014
On a conjecture of De Giorgi related to homogenization
Aram Karakhanyan, Henrik Shahgholian
For a periodic vector field , let solve the dynamical system \begin{equation*} \frac{d{\bf X}^ε}{dt} = {\bf F}\left(\frac {{\bf X}^ε}ε\right) . \end{equation*} I…
math.AP2014
An inverse problem for the refractive surfaces with parallel lighting
Aram Karakhanyan
In this article we examine the regularity of two types of weak solutions to a Monge-Ampère type equation which emerges in a problem of finding surfaces that refract coaxial light r…