Geodesic
A geometric maximum principle for variational problems in spaces of vector valued functions of bounded variation
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 41, Tome 385 (2010), pp. 5-17

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We discuss variational integrals with density having linear growth on spaces of vector valued $BV$-functions and prove $\operatorname{Im}(u)\subset K$ for minimizers $u$ provided that the boundary data take their values in the closed convex set $K$ assuming in addition that the integrand satisfies natural structure conditions. Bibl. 14 titles. 
@article{ZNSL_2010_385_a0,
     author = {M. Bildhauer and M. Fuchs},
     title = {A geometric maximum principle for variational problems in spaces of vector valued functions of bounded variation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--17},
     publisher = {mathdoc},
     volume = {385},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_385_a0/}
}
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M. Bildhauer; M. Fuchs. A geometric maximum principle for variational problems in spaces of vector valued functions of bounded variation. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 41, Tome 385 (2010), pp. 5-17. http://geodesic.mathdoc.fr/item/ZNSL_2010_385_a0/