N. S. Dairbekov, O. M. Penkin, D. Savasteev, “Harnack's inequality for harmonic functions on stratified sets”, Sibirsk. Mat. Zh., 2023, Volume 64, Number 5,Pages <nobr>971

Harnack's inequality for harmonic functions on stratified sets

N. S. Dairbekov^ab, O. M. Penkin^ac, D. Savasteev^c

^a Institute of Mathematics, Ministry of Education and Science of the Republic of Kazakhstan, Almaty
^b Suleyman Demirel University, Kaskelen, Almaty
^c Voronezh State University

Abstract: We prove Harnack's inequality for nonnegative harmonic functions in the sense of the “soft” Laplacian on a stratified set with flat strata.

Keywords: soft Laplacian, stratified measure, mean value theorem.

UDC: 517.956.2

MSC: 35R30

Received: 01.03.2023
Revised: 27.07.2023
Accepted: 02.08.2023

DOI: 10.33048/smzh.2023.64.506