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Improved regularity of solutions to elliptic equations involving Jacobians and applications. (English) Zbl 0831.35025
Various extensions of the so-called Wente’s estimate are proposed here. Our generalizations include the variable coefficients case, Neumann boundary conditions and modified Jacobians. Our main result shows that the constants in the estimates can be chosen independently of the domain on which the problem is posed. Several applications are given. These include regularity results for the solution to the equation of surfaces of prescribed mean curvature, and uniqueness for harmonic maps from surfaces into spheres.

##### MSC:
 35B65 Smoothness and regularity of solutions to PDEs 35J60 Nonlinear elliptic equations 42B25 Maximal functions, Littlewood-Paley theory 42B30 $$H^p$$-spaces