<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Hölder continuity of singular parabolic equations with variable nonlinearity

Laboratory of Mathematical Analysis and Applications, Department of Mathematics

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Hölder continuity of singular parabolic equations with variable nonlinearity"}

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...

Hölder continuity of singular parabolic equations with variable nonlinearity

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
Nonlinear parabolic equations, singular equations, variable nonlinearity, regularity of solutions

© 2020 Hamid El Bahja, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Hölder continuity of singular parabolic equations with variable nonlinearity

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

KeywordsNonlinear parabolic equations, singular equations, variable nonlinearity, regularity of solutions

© 2020 Hamid El Bahja, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Nonlinear parabolic equations, singular equations, variable nonlinearity, regularity of solutions