Functional Analysis and Its Applications

, Volume 52, Issue 1, pp 62–65 | Cite as

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

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Abstract

It is shown that, for any compact set K ⊂ ℝ n (n ⩾ 2) of positive Lebesgue measure and any bounded domain GK, there exists a function in the Hölder class C1,1(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.

Key words

minimal surface equation Hölder class removable set nonlinear mapping Schauder theorem fixed point 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of MathematicsNational Academy of Sciences of UkraineKievUkraine

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