On Singular Points of Solutions of the Minimal Surface Equation on Sets of Positive Measure

It is shown that, for any compact set K ⊂ ℝ n ( n ⩾ 2) of positive Lebesgue measure and any bounded domain G ⊃ K , there exists a function in the Hölder class C 1,1 ( G ) that is a solution of the minimal surface equation in G \ K and cannot be extended from G \ K to G as a solution of this equation...

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Bibliographic Details
Published in:Functional analysis and its applications 2018, Vol.52 (1), p.62-65
Main Author: Pokrovskii, A. V.
Format: Article
Language:English
Subjects:
Analysis
Brief Communications
Functional Analysis
Mathematics
Mathematics and Statistics
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Summary:It is shown that, for any compact set K ⊂ ℝ n ( n ⩾ 2) of positive Lebesgue measure and any bounded domain G ⊃ K , there exists a function in the Hölder class C 1,1 ( G ) that is a solution of the minimal surface equation in G \ K and cannot be extended from G \ K to G as a solution of this equation.
ISSN:0016-2663
1573-8485
DOI:10.1007/s10688-018-0209-4