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 Funktsional. Anal. i Prilozhen.: Year: Volume: Issue: Page: Find

 Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 1, Pages 76–79 (Mi faa3446)

Brief communications

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

A. V. Pokrovskii

Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine

Abstract: 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.

DOI: https://doi.org/10.4213/faa3446

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English version:
Functional Analysis and Its Applications, 2018, 52:1, 62–65

Bibliographic databases:

UDC: 517.956

Citation: A. V. Pokrovskii, “On Singular Points of Solutions of the Minimal Surface Equation on Sets of Positive Measure”, Funktsional. Anal. i Prilozhen., 52:1 (2018), 76–79; Funct. Anal. Appl., 52:1 (2018), 62–65

Citation in format AMSBIB
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