Bounds and regularity of Solutions of Planar Div-curl Problems
  New 2-norm bounds for solutions of planar div-curl boundary value problems on bounded planar regions are described. Prescribed flux, tangential trace and mixed boundary boundary are treated. A harmonic decomposition is used to separate components of the solution due to source terms from the components due to boundary data. Estimates for the solutions are obtained and some regularity results are described 
Giles Auchmuty
math.AP