Nonlinear degenerate p(x)-Laplacian equation with singular gradient and lower order term
Hichem Khelifi () and
Mohamed Amine Zouatini ()
Additional contact information
Hichem Khelifi: University of Algiers 1
Mohamed Amine Zouatini: Laboratory LEDPNL, ENS-Kouba
Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 1, 46-66
Abstract:
Abstract The present paper aims to study the Dirichlet problem for a nonlinear degenerate elliptic equation with singular gradient lower order term, we establish existence and regularity estimates for weak solutions of $$p(x)-$$ p ( x ) - Laplacian type elliptic equations of the form 0.1 $$\begin{aligned} \left\{ \begin{array}{ll} -\text {div}\left( \frac{\vert \nabla u\vert ^{p(x)-2}\nabla u}{(1+\vert u\vert )^{\gamma (x)}}\right) +\frac{\vert \nabla u\vert ^{p(x)}}{\vert u\vert ^{\theta }}=f+u^{r(x)} &{}\quad \hbox {in}\; \Omega , \\ u =0 &{} \quad \hbox {on}\; \partial \Omega , \end{array} \right. \end{aligned}$$ - div | ∇ u | p ( x ) - 2 ∇ u ( 1 + | u | ) γ ( x ) + | ∇ u | p ( x ) | u | θ = f + u r ( x ) in Ω , u = 0 on ∂ Ω , where $$\Omega $$ Ω is a bounded open subset in $${\mathbb {R}}^{N}$$ R N , $$0
Keywords: Nonlinear elliptic equations; Singular gradient lower order term; Degenerate coercivity; Existence and regularity; Harnack inequality; 35J62; 35J70; 35J75 (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:
Downloads: (external link)
http://link.springer.com/10.1007/s13226-023-00460-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:56:y:2025:i:1:d:10.1007_s13226-023-00460-9
Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226
DOI: 10.1007/s13226-023-00460-9
Access Statistics for this article
Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke
More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().