Manifold Constrained Variational Problems

B. Dacorogna, I. Fonseca, J. Malý, K. Trivisa

Abstract:

The integral representation for the relaxation of a class of energy functionals where the admissible fields are constrained to remain on a tex2html_wrap_inline192 m-dimensional manifold tex2html_wrap_inline196 is obtained. If tex2html_wrap_inline198 is a continuous function satisfying tex2html_wrap_inline200 for tex2html_wrap_inline202 and for all tex2html_wrap_inline204 then

eqnarray184

where tex2html_wrap_inline206 is open, bounded, and tex2html_wrap_inline208 is the tangential quasiconvexification of f at tex2html_wrap_inline212 tex2html_wrap_inline214 belong to the tangent space to tex2html_wrap_inline216 at tex2html_wrap_inline218



Get the paper in its entirety as