| Given a function 4 and s ∈ (0, 1), we will study the solutions of the following obstacle problem 1.u≥4 inRn 2.-D su≥0in Rn 3.-D sux =0forthose xsuchthat ux>4 x 4.lim x→+infinity ux=0 We show that when 4 is C1,s or smoother, the solution u is in the space C 1,alpha for every alpha < s. In the case that the contact set {lcub}u = 4 {rcub} is convex, we prove the optimal regularity result u ∈ C1,s. When 4 is only C1,beta for a beta < s, we prove that our solution u is C 1,alpha for every alpha < beta. |
