Harmonic homeomorphisms of the closed disc to itself need be in $W^\{1,p\}$, $p<2$, but not $W^\{1,2\}$
Harmonic homeomorphisms of the closed disc to itself need be in $W^\{1,p\}$, $p<2$, but not $W^\{1,2\}$
Harmonic maps $u$ from the closed disc onto bounded convex sets of the plane obey $u\in W^{1,p}, p<2$.