Quality theorems on the solutions of quasilinear second-order parabolic equations with discontinuous coefficients

Document Type : Research Paper

Author

Baku State University, Baku, Azerbaijan.

Abstract

A class of quasilinear second-order parabolic equations with discontinuous coefficients is considered in this work. The analog of Harnack inequality is proved for the non-negative solutions of these equations.

Keywords

Main Subjects

References

  • [1] S. T. Huseynov, Harnack type inequality for non-negative solutions of second order degenerate parabolic equations in divergent form, Electronic journal of Differential Equations, 2016(278) (2016), 1–11.
  • [2] N. V. Krylov and M.V. Safonov, Some properties of the solutions of parabolic equations with measurable coefficients, Izv. AN SSSR. Ser.matem., 44 (1980), 161–175.
  • [3] E. M. Landis, Second order equations of elliptic and parabolic types, Nauka, (1971), 288.
  • [4] O. A. Ladyzhenskaya and N. N. Uraltseva, On Holder norm estimates for the solutions of quasilinear elliptic equations in nondivergence form, Uspexi mat. nauk, 35(4) (1980), 144–145.
  • [5] I. T. Mamedov, On a priori estimate of the Holder norm for the solutions of quasilinear parabolic equations with discontinuous coefficients, Dokl. AN SSSR, 252(5) (1980), 1052–1054.
  • [6] A. A. Novruzov, On Holder norm estimate for the solutions of quasilinear elliptic equations with discontinuous coefficients, Dokl. AN SSSR, 253(1) (1980), 31-33.
  • [7] N. S. Trudinger, Local estimates for subsolutions and supersolutions of general second order elliptic quasilinear equations, Invent. Math., 61 (1980), 67–79.
Computational Methods for Differential Equations
Volume 12, Issue 4
October 2024
Pages 703-709

Files

History

  • Receive Date: 20 June 2023
  • Accept Date: 03 March 2024

Share

How to cite

Statistics