Generalised elliptic boundary problems

For elliptic systems of differential equations on a manifold with boundary, we prove the Fredholm property of a class of boundary problems which do not satisfy the Shapiro–Lopatinskii property. We name these boundary problems generalised elliptic, for they preserve the main properties of elliptic boundary problems. Moreover, they reduce to systems of pseudodifferential operators on the boundary which are generalised elliptic in the sense of Saks [R.S. Saks, On properties of generalised elliptic pseudodifferential operators on closed manifolds, Zap. Nauchn. Sem. LOMI 243 (1997) 215–269].