Asymptotic behavior of the spectrum of variational problems on the solutions of elliptic systems

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.