On elliptic equations in a half space or in convex wedges with irregular coefficients

الأصل · EN

We consider second-order elliptic equations in a half space with leading coefficients measurable in a tangential direction. We prove the W²ₚ-estimate and solvability for the Dirichlet problem when p∈ (1,2], and for the Neumann problem when p∈ [2,∞). We then extend these results to equations with more general coefficients, which are measurable in a tangential direction and have small mean oscillations in the other directions. As an application, we obtain the W²ₚ-solvability of elliptic equations in convex wedge domains or in convex polygonal domains with discontinuous coefficients.