<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

Publié en ligne: 28 déc. 2020

Pages: 51 - 82

Reçu: 10 sept. 2019

Accepté: 18 déc. 2019

DOI: https://doi.org/10.2478/auom-2020-0034

Mots clés
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

Publié en ligne: 28 déc. 2020

Pages: 51 - 82

Reçu: 10 sept. 2019

Accepté: 18 déc. 2019

DOI: https://doi.org/10.2478/auom-2020-0034

Mots clésNonlinear 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.

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