AbstractLet and be annuli in . Let , and assume that is the class of Sobolev homeomorphisms of onto . Then, we consider the following Dirichlet‐type energy of :
We prove that this energy integral attains its minimum for and , and the minimum is a certain radial diffeomorphism .For general , we minimize the Dirichlet‐type integral throughout the class of radial mappings between given annuli, and this minimum always exists for . For , the image annulus cannot be too thick, which is opposite to the Nitsche‐type phenomenon known for the standard Dirichlet energy, where the image annulus cannot be too thin.
