Submitted Paper
Inserted: 9 mar 2023
Last Updated: 14 feb 2025
Year: 2023
Notes:
Revised version.
Abstract:
A relaxation problem for maps from 3-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, lower semicontinuity of the extended energy, and strong approximation properties on Cartesian currents.
Keywords: relaxation, currents, Laplacean, mapping into the sphere
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