Geodesic
Asymptotic behavior of the spectrum of variational problems on the solutions of elliptic systems
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 23-39

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One computes the principal term of the asymptotics of the spectrum of variational problems of the form $B[u]/A[u]$ considered on the solutions of elliptic systems $Lu=0$ on a compact manifold with boundary. Previously, the corresponding result has been obtained by the authors under the additional condition of the existence of an elliptic boundary problem for the operator $L$. Now this restriction is removed. 
@article{ZNSL_1982_115_a2,
     author = {M. Sh. Birman and M. Z. Solomyak},
     title = {Asymptotic behavior of the spectrum of variational problems on the solutions of elliptic systems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {23--39},
     publisher = {mathdoc},
     volume = {115},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a2/}
}
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M. Sh. Birman; M. Z. Solomyak. Asymptotic behavior of the spectrum of variational problems on the solutions of elliptic systems. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 14, Tome 115 (1982), pp. 23-39. http://geodesic.mathdoc.fr/item/ZNSL_1982_115_a2/