ON CHARACTERIZATION OF A SYSTEM OF MINIMAL DIFFERENTIAL OPERATORS BY A PRIORI ESTIMATES IN THE SOBOLEV SPACES

In this paper we provide results on the characterization of elliptic and 𝑙-quasielliptic systems of minimal differential operators by a priori estimates in isotropic and anisotropic Sobolev spaces 𝑊𝑙 𝑝,0(R𝑛), 𝑝 ∈ [1,∞]. Fora 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 𝑊𝑙 𝑝,0(R𝑛), 𝑝 ∈ [1,∞], nonelliptic, and nonquasielliptic systems.Keywords: a priori estimate, differential operator, coercivity, Sobolev space, tensor product.