Partial differential equations - W2,2-solvability of the Dirichlet probeem for a class of elliptic equations with discontinuous coefficients, by FLAVIA GIANNETTI and GIOCONDA MOSCARIELLO, communicated on April 20, 2018

We study the Dirichlet problem for the second order elliptic equation (Equation presented) in a bounded regular domain Ω ⊂ ℝN, N > 2. We assume that f ∈ L2 and that the coefficients aij are measurable and bounded functions with the first derivatives in the Marcinkiewicz class weak-LN and having a sufficiently small distance to L∞. Under these assumptions we prove the solvability of the problem in W2,2 ∩ W1,2∗ 0, where 2∗ =2N/N-2. An higher integrability result for the gradient of the solution is achieved when f∈LP,p>2. © 2018 European Mathematical Society Publishing House. All rights reserved.