Geodesic
On Singular Points of Solutions of the Minimal Surface Equation on Sets of Positive Measure
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 1, pp. 76-79

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It is shown that, for any compact set $K\subset\mathbb{R}^n$ ($n\ge 2$) of positive Lebesgue measure and any bounded domain $G\supset K$, there exists a function in the Hölder class $C^{1, 1}(G)$ that is a solution of the minimal surface equation in $G\setminus K$ and cannot be extended from $G\setminus K$ to $G$ as a solution of this equation.
Keywords: minimal surface equation, Hölder class, removable set, nonlinear mapping, Schauder theorem, fixed point. 
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     author = {A. V. Pokrovskii},
     title = {On {Singular} {Points} of {Solutions} of the {Minimal} {Surface} {Equation} on {Sets} of {Positive} {Measure}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {76--79},
     publisher = {mathdoc},
     volume = {52},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2018_52_1_a8/}
}
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A. V. Pokrovskii. On Singular Points of Solutions of the Minimal Surface Equation on Sets of Positive Measure. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 1, pp. 76-79. http://geodesic.mathdoc.fr/item/FAA_2018_52_1_a8/