N. S. Dairbekov, O. M. Penkin, D. Savasteev, “Perron's method in the Dirichlet problem for the soft Laplacian on a stratified set”, Dokl. RAN. Math. Inf. Proc. Upr., 2025, Volume 521,Pages <nobr>23

MATHEMATICS

Perron's method in the Dirichlet problem for the soft Laplacian on a stratified set

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

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

Abstract: We prove solvability of the Dirichlet problem for the soft Laplacian on a stratified set basing on a modification of the Perron well-known method.

Keywords: stratified measure, soft Laplacian, mean value theorem, Harnack's inequality, Harnack convergence theorem.

UDC: 517.958

Presented: I. A. Taimanov
Received: 12.12.2024
Revised: 20.01.2025
Accepted: 20.01.2025

DOI: 10.31857/S2686954325010038