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Mathematics in Engineering

2021, Volume 3, Issue 3: 1-11. doi: 10.3934/mine.2021020
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On the Harnack inequality for non-divergence parabolic equations

  • 1.
    Dipartimento di Matematica "F. Casorati", Università di Pavia, via Ferrata 1, 27100 Pavia, Italy
  • 2.
    Dipartimento di Matematica "F. Brioschi", Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano, Italy
  • Received: 11 December 2019 Accepted: 29 May 2020 Published: 15 July 2020

  • In this paper we propose an elementary proof of the Harnack inequality for linear parabolic equations in non-divergence form.

    Citation: Ugo Gianazza, Sandro Salsa. On the Harnack inequality for non-divergence parabolic equations[J]. Mathematics in Engineering, 2021, 3(3): 1-11. doi: 10.3934/mine.2021020

    Related Papers:

  • In this paper we propose an elementary proof of the Harnack inequality for linear parabolic equations in non-divergence form.


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    [1] Imbert C, Silvestre L (2013) An introduction to fully nonlinear parabolic equations, In: An Introduction to the Kähler-Ricci Flow, Cham: Springer, 7-88.
    [2] Krylov NV (1983) Boundedly inhomogeneous elliptic and parabolic equations in a domain. Izv Akad Nauk SSSR Ser Mat 47: 75-108.
    [3] Krylov NV (1987) Nonlinear Elliptic and Parabolic Equations of the Second Order, Dordrecht: D. Reidel Publishing Co.
    [4] Krylov NV, Safonov MV (1980) A property of the solutions of parabolic equations with measurable coefficients. Izv Akad Nauk SSSR Ser Mat 44: 161-175.
    [5] Ladyzenskaja OA, Solonnikov VA, Ural'tzeva NN (1967) Linear and Quasilinear Equations of Parabolic Type, Providence: American Mathematical Society.
    [6] Landis EM (1968), Harnack's inequality for second order elliptic equations of Cordes type. Dokl Akad Nauk SSSR 179: 1272-1275.
    [7] Landis EM (1998) Second Order Equations of Elliptic and Parabolic Type, Providence: American Mathematical Society.
    [8] Lieberman GM (1996) Second Order Parabolic Differential Equations, World Scientific.
    [9] Safonov MV (1980) Harnack's inequality for elliptic equations and Hölder property of their solutions. Zap Nauchn Sem Leningrad Otdel Mat Inst Steklov 96: 272-287.
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  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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