Inserted: 9 mar 2023
Last Updated: 9 mar 2023
A relaxation problem for maps from n-dimensional domains into the unit 2-sphere is analysed, the energy being given in the smooth case by the integral of the modulus of the Laplacean vector. For second order Sobolev maps, a complete explicit formula of the relaxed energy is obtained. Our proof is based on the following results: minimal energy computation of maps with fixed degree, Dipole-like problems, density of maps with small singular sets, lower semicontinuity of the extended energy, and strong approximation properties on Cartesian currents.