3 citations · 11 across the 30 of their papers we have counts for
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On the weak formulation of Prandtl's minimum drag problem
Aram L. Karakhanyan, Yigit Katgi
We study Prandtl's classical problem on minimising the induced drag for a finite wing with fixed span. The induced drag is given by a singular quadratic functional of the circulati…
A Monotonicity formula for almost self-similar suitable weak solutions to the stationary Navier-Stokes equations in
Yucong Huang, Aram Karakhanyan
In this paper we show that a suitable weak solution to the stationary Navier-Stokes system in , cannot behave like a self-similar function of degree negative one if th…
A monotonicity formula for a classical free boundary problem
Aram Karakhanyan
We construct a monotonicity formula for the free boundary problem of the form , where is a Radon measure. It implies that the blow up limits of solutions are homogenous f…
A new monotonicity formula for quasilinear elliptic free boundary problems
Aram Karakhanyan
We construct a monotonicity formula for a class of free boundary problems associated with the stationary points of the functional \[ J(u)=\int_ΩF(|\nabla u|^2)+\mbox{meas}(\{u>0\}\…
On the three-dimensional shape of a crystal
Emanuel Indrei, Aram Karakhanyan
In this paper we completely settle the Almgren problem in under some generic conditions on the potential and tension functions. The problem, among other things, appea…
Stable cones in the Alt-Phillips free boundary problem
Aram Karakhanyan, Tomás Sanz-Perela
In this paper we prove a classification result for axially symmetric one phase minimizers of the Alt-Phillips free boundary problem in dimensions 3, 4, and 5. To accomplish this, w…