Email this article On Singular Points of Solutions of the Minimal Surface Equation on Sets of Positive Measure
- Authors: Pokrovskii A.V.1
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Affiliations:
- Institute of Mathematics, National Academy of Sciences of Ukraine
- Issue: Vol 52, No 1 (2018)
- Pages: 62-65
- Section: Brief Communications
- URL: https://journal-vniispk.ru/0016-2663/article/view/234409
- DOI: https://doi.org/10.1007/s10688-018-0209-4
- ID: 234409
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Abstract
It is shown that, for any compact set K ⊂ ℝn (n ⩾ 2) of positive Lebesgue measure and any bounded domain G ⊃ K, 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.
About the authors
A. V. Pokrovskii
Institute of Mathematics, National Academy of Sciences of Ukraine
Author for correspondence.
Email: pokrovsk@imath.kiev.ua
Ukraine, Kiev
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