arXiv subjects

Vincent Millot

Publications and source records attributed to Vincent Millot.

20 records · Page 2Linked to original sources

arXiv2008

Homogenization of variational problems in manifold valued BV-spaces

This paper extends the result of \cite{BM} on the homogenization of integral functionals with linear growth defined for Sobolev maps taking values in a given manifold. Through a $Γ$-convergence analysis, we identify the homogenized energy in the space of functions of bounded variation. It turns out to be finite for $BV$-maps with values in the manifold. The bulk and Cantor parts of the energy involve the tangential homogenized density introduced in \cite{BM}, while the jump part involves an homogenized surface density given by a geodesic type problem on the manifold.

math.AP↗

arXiv2008

Homogenization of variational problems in manifold valued Sobolev spaces

Homogenization of integral functionals is studied under the constraint that admissible maps have to take their values into a given smooth manifold. The notion of tangential homogenization is defined by analogy with the tangential quasiconvexity introduced by Dacorogna, Fonseca, Maly and Trivisa \cite{DFMT}. For energies with superlinear or linear growth, a $Γ$-convergence result is established in Sobolev spaces, the homogenization problem in the space of functions of bounded variation being the object of \cite{BM}.

math.AP↗