Spectrum asymptotics for one “nonsmooth” variational problem with solvable constraint

In a previous paper by Birman and Filonov, the spectrum of the Maxwell operator with nonsmooth coefficients in Lipschitz domains was investigated. The claim that its eigenvalues obey the Weyl asymptotics was proved up to a statement about the spectrum of an auxiliary problem with constraint. The proof of that statement is given in the present paper.