2025/02/20 by Fessel Achhoud, Achhoud, Fessel, Abdelkader Bouajaja +3
Computer Science · Engineering · Mathematics · #35J60 #35K05 #35K67 #35R09 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2502.14492
openalex publication_date 2025/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using an approach by contradiction we prove the existence and uniqueness of a weak solution to a quasi-linear elliptic boundary value problem with singular convection term and Hardy Potential. Whose simplest model is \Scale[0.8]\ds u ∈ W01,2(O)∩ L^∞(O) : -Δu=-Adiv((x)/(\vert x\vert2)u)+λ(u)/(\vert x\vert2)+f(x), where \(O\) is a bounded open set in \(ℝN\), (A,λ) ∈ (0, ∞)2 and \(f∈ W-1,2(O)\). Additionally, by taking advantage of the regularizing effect of the interaction between the coefficient of the zero order term and the datum, we establish the existence, uniqueness and regularity of a weak solution to a quasi-linear boundary value problem whose simplest example is \Scale[0.8]\ds u ∈ W01,2(O)∩ L^∞(O) : -Δu +a(x)\vert u\vertp-2u=-Adiv((x)/(\vert x\vert2)u)+λ(u)/(\vert x\vert2)+f(x), under suitable assumptions on a and f.