Integral Estimates of Solutions to Boundary Values Problems for the Poisson Equation

F. G. Avkhadiev; A. R. Kacimov

doi:10.3103/S1066369X23100018

Integral Estimates of Solutions to Boundary Values Problems for the Poisson Equation

F. G. Avkhadiev^*, A. R. Kacimov^*

^*Corresponding author for this work

Soils, Water and Agricultural Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	63-69
Number of pages	7
Journal	Russian Mathematics
Volume	67
Issue number	10
DOIs	https://doi.org/10.3103/S1066369X23100018
Publication status	Published - Oct 2023

Keywords

Dirichlet problem
Poisson equation
isoperimetric inequality
mixed boundary value problem

ASJC Scopus subject areas

General Mathematics

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10.3103/S1066369X23100018

Cite this

@article{14e56e62018344af92fba670dfe29407,

title = "Integral Estimates of Solutions to Boundary Values Problems for the Poisson Equation",

abstract = "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 = "Dirichlet problem, Poisson equation, isoperimetric inequality, mixed boundary value problem",

author = "Avkhadiev, {F. G.} and Kacimov, {A. R.}",

note = "Publisher Copyright: {\textcopyright} 2023, Allerton Press, Inc.",

year = "2023",

month = oct,

doi = "10.3103/S1066369X23100018",

language = "English",

volume = "67",

pages = "63--69",

journal = "Russian Mathematics",

issn = "1066-369X",

publisher = "Allerton Press Inc.",

number = "10",

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T1 - Integral Estimates of Solutions to Boundary Values Problems for the Poisson Equation

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AU - Kacimov, A. R.

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Y1 - 2023/10

N2 - 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.

AB - 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.

KW - Dirichlet problem

KW - Poisson equation

KW - isoperimetric inequality

KW - mixed boundary value problem

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JO - Russian Mathematics

JF - Russian Mathematics

IS - 10

ER -

Integral Estimates of Solutions to Boundary Values Problems for the Poisson Equation

Abstract

Keywords

ASJC Scopus subject areas

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