F. G. Avkhadiev, A. R. Kacimov, “Integral estimates of solutions to boundary values problems for the Poisson equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, Number 10,Pages <nobr>70

Brief communications

Integral estimates of solutions to boundary values problems for the Poisson equation

F. G. Avkhadiev^a, A. R. Kacimov^b

^a Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
^b Sultan Qaboos University, Al-Khod 123, PO Box 34, Sultanate Oman

Abstract: We consider solutions to two boundary values problems for the Poisson equation on plane domains. We prove several estimates for integrals of solutions using geometric characteristics of domains.

Keywords: Poisson equation, Dirichlet problem, boundary values problem, isoperimetric inequality.

UDC: 517.95

Received: 10.07.2023
Revised: 19.07.2023
Accepted: 26.09.2023

DOI: 10.26907/0021-3446-2023-10-70-76