Hölder continuity of singular parabolic equations with variable nonlinearity
Dec 28, 2020
About this article
Published Online: Dec 28, 2020
Page range: 51 - 82
Received: Sep 10, 2019
Accepted: Dec 18, 2019
DOI: https://doi.org/10.2478/auom-2020-0034
Keywords
© 2020 Hamid El Bahja, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
In this paper we obtain the local Hölder regularity of the weak solutions for singular parabolic equations with variable exponents. The proof is based on DiBenedetto’s technique called intrinsic scaling; by choosing an appropriate geometry one can deduce energy and logarithmic estimates from which one can implement an iterative method to obtain the regularity result.