Electron. J. Differential Equations, Vol. 2019 (2019), No. 104, pp. 1-21.

Regularity for anisotropic quasi-linear parabolic equations with variable growth

Hamid El Bahja

In this article, we study a class of anisotropic quasi-linear parabolic equations with variable exponents. Following DiBenedetto's intrinsic scaling method, we prove local continuity of solutions under the condition for which only local boundedness was known.

Submitted July 10, 2018. Published September 10, 2019.
Math Subject Classifications: 35K20, 35K65, 35B45.
Key Words: Anisotropic parabolic problems; regularity theory; intrinsic scaling.

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Hamid El Bahja
Laboratory of Mathematical Analysis and Applications
CeReMAR, Department of Mathematics, P.O. Box 1014
Faculty of Sciences, Mohammed V University, Rabat, Morocco
email: hamidsm88@gmail.com

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