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Glasnik matematički, Vol. 57 No. 1, 2022.

Original scientific paper

https://doi.org/10.3336/gm.57.1.03

Hölder continuity for the solutions of the p(x)-Laplace equation with general right-hand side

Abdeslem Lyaghfouri orcid id orcid.org/0000-0002-0957-9675 ; Department of Mathematical Sciences, United Arab Emirates University, Al Ain, Abu Dhabi, UAE

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page 35-47

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Abstract

We show that bounded solutions of the quasilinear elliptic equation
\(\Delta_{p(x)} u=g+div(\textbf{F})\) are locally Hölder continuous
provided that the functions \(g\) and \(\textbf{F}\) are in suitable
Lebesgue spaces.

Keywords

\(p(x)\)-Laplacian, Hölder continuity

Hrčak ID:

279798

URI

https://hrcak.srce.hr/279798

Publication date:

28.6.2022.

Visits: 323 *

Publication date: 30 June 2022

Volume: Vol 57

Issue: Svezak 1

Pages: 35-47

DOI: https://doi.org/10.3336/gm.57.1.03

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: \(p(x)\)-Laplacian, Hölder continuity

Hölder continuity for the solutions of the p(x)-Laplace equation with general right-hand side

Abdeslem Lyaghfouri[1]

Email: a.lyaghfouri@uaeu.ac.ae

 

[1] Department of Mathematical Sciences, United Arab Emirates University, Al Ain, Abu Dhabi, UAE

Abstract

We show that bounded solutions of the quasilinear elliptic equation \(\Delta_{p(x)} u=g+div(\textbf{F})\) are locally Hölder continuous provided that the functions \(g\) and \(\textbf{F}\) are in suitable Lebesgue spaces.

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