The Dirichlet energy of Sobolev mappings between Riemannian manifolds is studied. After giving an explicit formula of the polyconvex extension of the energy for currents between manifolds, we prove a strong density result. As a consequence, we give an explicit formula for the relaxed energy. The fractional space of traces of W 1,2-mappings is also treated.
The Relaxed Dirichlet Energy of Manifolds Constrained Mappings / M. GIAQUINTA; G. MODICA; D. MUCCI. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - STAMPA. - 1:(2008), pp. 1-51. [10.1515/ACV.2008.001]
The Relaxed Dirichlet Energy of Manifolds Constrained Mappings
GIAQUINTA, MARIANO;MODICA, GIUSEPPE;
2008
Abstract
The Dirichlet energy of Sobolev mappings between Riemannian manifolds is studied. After giving an explicit formula of the polyconvex extension of the energy for currents between manifolds, we prove a strong density result. As a consequence, we give an explicit formula for the relaxed energy. The fractional space of traces of W 1,2-mappings is also treated.
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