Remarks on the thin obstacle problem and constrained Ginibre ensembles

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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 H1(R2) which improves previous results in H1loc(R2).
Original languageEnglish
Pages (from-to)616-627
Number of pages11
JournalCommunications in partial differential equations
Issue number4
Early online date14 May 2018
Publication statusE-pub ahead of print - 14 May 2018


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