Abstract: This paper is concerned with the regularity of minimum solution u of the following functional
L(u)=∫₀a_αβ(x)g_ij(u)D_auⁱD_βvⁱdx
on the restraint E={u∈W₀^1,2(Ω,R^N)||u|_Lp=1}Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Hölder continuous.