Geodesic
Some Remarks on the (Non-) Attainment of the Boundary Data for Variational Problems in the Space BV
Journal of convex analysis, Tome 25 (2018) no. 1, pp. 219-223
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We discuss the standard relaxed version of a minimization problem for variational integrals of linear growth together with prescribed Dirichlet boundary data $u_0$ and give estimates for the size of the set $\{x \in \partial \Omega : u (x) \not= u_0 (x)\}$ for BV-minimizers $u$ which imply $$ {\cal{H}}^{n -1} \left(\left\{x \in \partial \Omega : u (x) u_0 (x)\right\}\right) = {\cal{H}}^{n - 1} \left(\left\{x \in \partial \Omega : u (x) > u_0 (x) \right\}\right) $$ in the case of minimal surfaces $u$ not attaining the boundary values $u_0$ on a subset of $\partial \Omega$ with positive measure.
Classification : 49J40, 49J45, 49Q05
Mots-clés : Variational problems of linear growth, boundary behaviour, minimal surfaces 
@article{JCA_2018_25_1_JCA_2018_25_1_a12,
     author = {M. Bildhauer and M. Fuchs},
     title = {Some {Remarks} on the {(Non-)} {Attainment} of the {Boundary} {Data} for {Variational} {Problems} in the {Space} {BV}},
     journal = {Journal of convex analysis},
     pages = {219--223},
     year = {2018},
     volume = {25},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_1_JCA_2018_25_1_a12/}
}
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M. Bildhauer; M. Fuchs. Some Remarks on the (Non-) Attainment of the Boundary Data for Variational Problems in the Space BV. Journal of convex analysis, Tome 25 (2018) no. 1, pp. 219-223. http://geodesic.mathdoc.fr/item/JCA_2018_25_1_JCA_2018_25_1_a12/