Nonlinear degenerate p(x)-Laplacian equation with singular gradient and lower order term

Hichem Khelifi () and Mohamed Amine Zouatini ()
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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
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DOI: 10.1007/s13226-023-00460-9

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