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Maximum Principle and Its Application to Elliptic Partial Differential Equations
Subject area: Physical Sciences and Environment · Area of research: Mathematics
DOI: 10.64388/IREV9I3-1710849-8560
Abstract
The most important tool that investigates most properties of solutions and equations of second order elliptic and parabolic type is the maximum principle. This has types, and all these types enable us to obtain valuable information about the properties of solutions and perhaps the equations themselves. Originating from the classical theory of harmonic functions, it has been generalized and extended to a wide range of elliptic partial differential equations and plays a critical role in proving uniqueness, comparism theorems, a priori estimates, and regularity results.
References
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How to cite this paper
@article{1710849,
author = {Okpanachi Sunday, Okpanachi George Echiye, Samuel Henry Owoicho, Ewaoche Nicholas},
title = {Maximum Principle and Its Application to Elliptic Partial Differential Equations},
journal = {Iconic Research And Engineering Journals},
year = {2025},
volume = {9},
number = {3},
pages = {1477-1484},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1710849.pdf},
abstract = {The most important tool that investigates most properties of solutions and equations of second order elliptic and parabolic type is the maximum principle. This has types, and all these types enable us to obtain valuable information about the properties of solutions and perhaps the equations themselves. Originating from the classical theory of harmonic functions, it has been generalized and extended to a wide range of elliptic partial differential equations and plays a critical role in proving uniqueness, comparism theorems, a priori estimates, and regularity results.},
month = {September},
doi = {https://doi.org/10.64388/IREV9I3-1710849-8560}
}