The p-energy of Sobolev mappings between Riemannian manifolds is studied, for each integer p greater than two. We analyse the lower semicontinuous extension of the energy to currents. We then restrict to mappings with values into the p-sphere, by giving an explicit relaxed p-energy formula, whose proof depends on a strong density result. Finally, a related coarea formula is obtained.
The relaxed p-energy of manifold constrained mappings / Mucci, D.. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. - ISSN 0009-725X. - 74:1(2025). [10.1007/s12215-024-01158-5]
The relaxed p-energy of manifold constrained mappings
Mucci D.
2025
Abstract
The p-energy of Sobolev mappings between Riemannian manifolds is studied, for each integer p greater than two. We analyse the lower semicontinuous extension of the energy to currents. We then restrict to mappings with values into the p-sphere, by giving an explicit relaxed p-energy formula, whose proof depends on a strong density result. Finally, a related coarea formula is obtained.
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