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JOURNALS // Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia // Archive

Dokl. RAN. Math. Inf. Proc. Upr., 2024 Volume 518, Pages 5–9 (Mi danma543)

MATHEMATICS

On removable singularities of harmonic functions on a stratified set

N. S. Dairbekovab, O. M. Penkinac, D. Savasteevc

a Institute of Mathematics and Mechanics, Kazakhstan National Academy of Sciences, Almaty, the Republic of Kazakhstan
b SDU University, Kaskelen, the Republic of Kazakhstan
c Voronezh State University

Abstract: We consider sets removable for bounded harmonic functions on a stratified set with flat interior strata. It is proved that relatively closed sets of finite Hausdorff $(n-2)$-measure are removable for bounded harmonic functions on an $n$-dimensional stratified set satisfying the strong sturdiness condition.

Keywords: stratified measure, soft Laplacian, mean value, Harnack inequality.

UDC: 517.596.2

Presented: I. A. Taimanov
Received: 26.05.2024
Revised: 21.06.2024
Accepted: 05.07.2024

DOI: 10.31857/S2686954324040015


 English version:
Doklady Mathematics, 2024, 110:1, 297–300

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© Steklov Math. Inst. of RAS, 2025