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 inFunctional analysis and its applications Vol. 52; no. 1; pp. 62 - 65
Main Author Pokrovskii, A. V.
Format Journal Article
LanguageEnglish
Published New York Springer US 2018
Springer Nature B.V
Subjects
Analysis
Brief Communications
Functional Analysis
Mathematics
Mathematics and Statistics
Schauder theorem
nonlinear mapping
minimal surface equation
Hölder class
fixed point
removable set
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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