Open sets of harmonicity for separately harmonic functions

Let D subset of R-N, G subset of R-M be two open sets, E subset of D and F subset of G two compact sets which satisfy the condition (H) (that is a harmonic condition similar to Leja's condition). We find an open set Omega subset of RN+M such that each separately harmonic function f : X := (D x F) boolean OR (E x G) --> R (i.e.: for all x in E, f(x,.) is harmonic on G; for all y in F, f(.,y) is harmonic on D) extends to a harmonic function on Omega.