Dirichlet Problems with Singular Convection Terms and Applications to Some Elliptic Systems

To be more precise, in [2] is proved the existence of u { weak solution belonging to W 1,2 0 (Ω) ∩ L ∗∗ (Ω), if m ≥ 2N N+2 (“Stampacchia” theory); distributional solution belonging to W 1,m ∗ 0 (Ω), if 1 < m < 2N N+2 (“Calderon-Zygmund” theory); (5) where m∗ = mN N−m (1 ≤ m < N) and m ∗∗ = mN N−2m (1 ≤ m < N 2 ). Note that the above existence results are exactly the results proved with E = 0 in [7] and [5]. The starting point is a nonlinear approach to a linear noncoercive problem. Then, in a more recent paper ([3]), dedicated to Thierry Gallouet, differential problems with vector fields E which do not belong to (L(Ω)) are considered. The first step is the study of the boundary value problem (1) if the main assumption of [2] is not satisfied and we assume