IMPROVED REGULARITY OF SOLUTIONS TO ELLIPTIC-EQUATIONS INVOLVING JACOBIANS AND APPLICATIONS

Various extensions of the so-called Wente's estimate are proposed here . Our generalizations include the variable coefficient case, Neumann b oundary conditions and modified jacobians. Our main result shows that the constants in the estimates can be chosen independently of the doma in on which the problem is posed. Several applications are given. Thes e include regularity results for the solution to the equation of surfa ces of prescribed mean curvature, and uniqueness for harmonic maps fro m surfaces into spheres.