Spectral asymptotics of elliptic strongly degenerate operators of arbitrary order

We compute the principal term of the spectral asymptotics for elliptic operators of an arbitrary order which is degenerate at the boundary of the domain. The degree of the degeneracy is such that the order of the decrease of the eigenvalues of the boundary-value problems is different from the classical one and the asymptotic coefficient depends on the form of the boundary conditions (strong degeneracy).