Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 104, pp. 1-21.

Title: Regularity for anisotropic quasi-linear parabolic equations with variable growth

Author: Hamid El Bahja (Mohammed V Univ., Rabat, Morocco)

Abstract:
 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.