2018/09/26 by Kalaj, David
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1809.09893
Given two annuli A(r,R) and A(r_∗, R_∗), in R3 equipped with the Euclidean metric and the weighted metric |y|-2 respectively, we minimize the Dirichlet integral, i.e. the functional \mathscrF[f] = ∫A(r,R) \frac\Vert Df\Vert2 |f|2, where f is a homeomorphism between A(r,R) and A(r_∗,R_∗), which belongs to the Sobolev class \mathscrW1,2. The minimizer is a certain generalized radial mapping, i.e. a mapping of the form f(|x|η)=ρ(|x|)T(η), where T is a conformal mapping of the unit sphere onto itself. It should be noticed that in this case no Nitsche phenomenon occur.