On Existence and Regularity of Solutions to a Class of Generalized Stationary Stokes Problem

We investigate existence of weak solutions and their smoothness properties for a type of generalized Stokes problem. The generalization we consider here consists in two points: A Laplacean is replaced by a general second order linear elliptic operator in divergence form and “pressure” gradient ∇p is replaced by a linear operator of the first order. Introduction Results contained in this contribution can be found with proofs in the preprint Huy and Stará [11]. Let Ω ⊂ R, (d ≥ 2), be a bounded domain with boundary ∂Ω. We study a generalization of linear Stokes problem: For given f = (f1, · · · , fd) : Ω −→ R d and g : Ω −→ R, A =