Geodesic
Removable Singularities of Solutions of the Minimal Surface Equation
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 4, pp. 62-68

Voir la notice de l'article provenant de la source Math-Net.Ru

Suppose that $G$ is a bounded domain in $\mathbb{R}^n$ ($n\ge 2$), $E\ne G$ is a relatively closed set in $G$, and $0\alpha1$. We prove that $E$ is removable for solutions of the minimal surface equation in the class $C^{1,\alpha}(G)_{\operatorname{loc}}$ if and only if the ($n-1+\alpha$)-dimensional Hausdorff measure of $E$ is zero.
Keywords: removable singularity, minimal surface, Hölder class, Hausdorff measure. 
@article{FAA_2005_39_4_a4,
     author = {A. V. Pokrovskii},
     title = {Removable {Singularities} of {Solutions} of the {Minimal} {Surface} {Equation}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {62--68},
     publisher = {mathdoc},
     volume = {39},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2005_39_4_a4/}
}
TY  - JOUR
AU  - A. V. Pokrovskii
TI  - Removable Singularities of Solutions of the Minimal Surface Equation
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2005
SP  - 62
EP  - 68
VL  - 39
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2005_39_4_a4/
LA  - ru
ID  - FAA_2005_39_4_a4
ER  - 
%0 Journal Article
%A A. V. Pokrovskii
%T Removable Singularities of Solutions of the Minimal Surface Equation
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2005
%P 62-68
%V 39
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2005_39_4_a4/
%G ru
%F FAA_2005_39_4_a4
A. V. Pokrovskii. Removable Singularities of Solutions of the Minimal Surface Equation. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 4, pp. 62-68. http://geodesic.mathdoc.fr/item/FAA_2005_39_4_a4/