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1710849PublishedVol 9 · Issue 3

Maximum Principle and Its Application to Elliptic Partial Differential Equations

Okpanachi Sunday Okpanachi George Echiye Samuel Henry Owoicho Ewaoche Nicholas

Subject area: Physical Sciences and Environment  ·  Area of research: Mathematics

DOI: https://doi.org/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.

How to cite this paper

Okpanachi Sunday, Okpanachi George Echiye, Samuel Henry Owoicho, Ewaoche Nicholas "Maximum Principle and Its Application to Elliptic Partial Differential Equations" Iconic Research And Engineering Journals Volume 9 Issue 3 2025 Page 1477-1484 https://doi.org/10.64388/IREV9I3-1710849-8560
Okpanachi Sunday, Okpanachi George Echiye, Samuel Henry Owoicho, Ewaoche Nicholas "Maximum Principle and Its Application to Elliptic Partial Differential Equations" Iconic Research And Engineering Journals, vol. 9, no. 3, Sep. 2025, doi: https://doi.org/10.64388/IREV9I3-1710849-8560
Okpanachi Sunday, Okpanachi George Echiye, Samuel Henry Owoicho, Ewaoche Nicholas (2025). Maximum Principle and Its Application to Elliptic Partial Differential Equations. Iconic Research And Engineering Journals, 9(3). doi: https://doi.org/10.64388/IREV9I3-1710849-8560
Okpanachi Sunday, Okpanachi George Echiye, Samuel Henry Owoicho, Ewaoche Nicholas "Maximum Principle and Its Application to Elliptic Partial Differential Equations" Iconic Research And Engineering Journals, vol. 9, no. 3, Sep. 2025. Crossref, https://doi.org/10.64388/IREV9I3-1710849-8560
@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}
  }