Hölder continuity of singular parabolic equations with variable nonlinearity
| 28 gru 2020
O artykule
Data publikacji: 28 gru 2020
Zakres stron: 51 - 82
Otrzymano: 10 wrz 2019
Przyjęty: 18 gru 2019
DOI: https://doi.org/10.2478/auom-2020-0034
Słowa kluczowe
© 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.