We obtain boundary estimates for the gradient of solutions to elliptic systems with Dirichlet or Neumann boundary conditions and L-1-data, under some condition on the divergence of the data. Similar boundary estimates are obtained for div-curl and Hodge systems.
Brezis, H., & Van Schaftingen, J. (2007). Boundary estimates for elliptic systems with L-1-data. Calculus of Variations and Partial Differential Equations, 30(3), 369-388. https://doi.org/10.1007/s00526-007-0094-9 (Original work published 2007)