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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

This contribution is part of the Special Issue: Critical values in nonlinear pdes – Special Issue dedicated to Italo Capuzzo Dolcetta
Guest Editor: Fabiana Leoni
Link: www.aimspress.com/mine/article/5754/special-articles

Special Issues: Critical values in nonlinear pdes - Special Issue dedicated to Italo Capuzzo Dolcetta

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

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.

© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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