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1710849 Vol 9 · Issue 3 Download Paper

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: 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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[4] Farrs, W. G. (1999) Partial Differential Equations. New York: Springer-Verlag.

[5] Gidas, B., Ni,Y-M and Nirenberg, L. ''Symmetry and Related Properties Via Maximum Principles'' Comm. Math. Phys., 68 (1979), 209-243.

[6] Murray H. Protter, Hans F. Weinberger, Maximum Principle in Differential Equations, Springer-Verlag, New York Berlin Heidelberg Tokyo, 1984

[7] Patricia Pucci and James Serrin, The Strong Maximum Principle Revisited.

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[9] Protter, M. H. and Weinberger, H. F., Maximum Principles in Differential Equations, (Prentice-Hall, New Jersey, U.S.A, 1967)

[10] Qing Han, A basic course in Partial Differential Equations, American Mathematical Society, Providence, Rhode Island, 2011.

[11] Rene P. Sperb, Maximum Principle and their Applications, Seminar fr Angewandte Mathematik Zurich Switzerland, Academic Press, New York London Toronto Sydney San Francisco, 1981

[12] Sattinger, D. H. (1972) Monotone Methods in Nonlinear Elliptic and Parabolic Boundary Value Problems. Indiana University Journal 2111: 917 - 1000.

[13] Serrin, J., ''A symmetry Problem in Potential Theory'''. Arch. Ration. Mech. Anal. 43 (1971), 304 - 318.

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[15] Troy, W. C., ''Symmetry Properties in Systems of Semilinear Elliptic Equations'' J. Diff. Equations, 42 (1981), 400-413.

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}
  }