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 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.
scientific article; zbMATH DE number 811429
scientific article