Regularity results for a class of obstacle problems in Heisenberg groups

We study regularity results for solutions u is an element of HW (1,p) (Omega) to the obstacle problem integral(Omega) A(x, del(H)u)del(H)(v - u) d x >= 0 for all(v) is an element of K-psi, (u) (Omega) such that u >= psi a.e. in Omega, where K-psi, (u) (Omega) = {v is an element of HW (1,p) (Omega): v - u is an element of HW0 (1,p) (Omega)v >= psi a.e in Omega}, in Heisenberg groups H (n) . In particular, we obtain weak differentiability in the T-direction and horizontal estimates of Calderon-Zygmund type, i.e. T psi is an element of HWloc1,p (Omega) double right arrow T u is an element of L-loc(p) (Omega), vertical bar del(H)psi vertical bar(p) is an element of L-loc(q) (Omega) double right arrow vertical bar del(H)u vertical bar(p) is an element of L-loc(q) (Omega), where 2 < p < 4, q > 1.