# Remarks on the thin obstacle problem and constrained Ginibre ensembles

@article{Karakhanyan2017RemarksOT,
title={Remarks on the thin obstacle problem and constrained Ginibre ensembles},
author={Aram L. Karakhanyan},
journal={Communications in Partial Differential Equations},
year={2017},
volume={43},
pages={616 - 627}
}
• A. Karakhanyan
• Published 1 February 2017
• Mathematics
• Communications in Partial Differential Equations
ABSTRACT We consider the problem of constrained Ginibre ensemble with prescribed portion of eigenvalues on a given curve Γ⊂ℝ2 and relate it to a thin obstacle problem. The key step in the proof is the H1 estimate for the logarithmic potential of the equilibrium measure. The coincidence set has two components: one in Γ and another one in ℝ2∖Γ which are well separated. Our main result here asserts that this obstacle problem is well posed in which improves previous results in .
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