On subordination conditions for systems of minimal di erential operators

In this paper, we provide a review of results on apriori estimates for systems of minimal differential operators in the scale of spaces \(L^p(Ω),\) where \(p∈[1,∞].\) We present results on the characterization of elliptic and \(l\)-quasielliptic systems using apriori estimates in isotropic and anisotropic Sobolev spaces \(Wp,0^l( R^n),\)\(p∈[1,∞].\) For a given set \(l=(l_1,,l_n)∈ N^n\) we prove criteria for the existence of \(l\)-quasielliptic and weakly coercive systems and indicate wide classes of weakly coercive in \(Wp,0^l( R^n),\) \(p∈[1,∞],\) nonelliptic, and nonquasielliptic systems. In addition, we describe linear spaces of operators that are subordinate in the \(L^∞( R^n)\)-norm to the tensor product of two elliptic differential polynomials.