On Subordination Conditions for Systems of Minimal Differential Operators

In this paper, we provide a review of results on a priori estimates for systems of minimal differential operators in the scale of spaces Lp(Ω), where p ∈ [1, ∞]. We present results on the characterization of elliptic and l-quasielliptic systems using a priori estimates in isotropic and anisotropic Sobolev spaces Wp,0lRn, p ∈ [1, ∞]. For a given set l = (l1,.., ln) ∈ Nn we prove criteria for the existence of l-quasielliptic and weakly coercive systems and indicate wide classes of weakly coercive in Wp,0lRn, p ∈ [1, ∞], nonelliptic, and nonquasielliptic systems. In addition, we describe linear spaces of operators that are subordinate in the L∞(Rn)-norm to the tensor product of two elliptic differential polynomials. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.