A Class of Non-linear Anisotropic Elliptic problems with Unbounded Coefficients and Singular Quadratic Lower Order Terms

2025/12/09 by Achhoud, Fessel, Khelifi, Hichem
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · doi:10.48550/arxiv.2512.08391

openalex publication_date 2025/12/09 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28

Abstract

In this work, we study the existence and regularity results of anisotropic elliptic equations with a singular lower order term that grows naturally with respect to the gradient and unbounded coefficients. We take up the following model problem \-∑_{j∈ J} D_j([ 1+ u^q]\vert D_ju\vert^p_j-2 D_ju)+∑_{j∈ J}\frac\vert D_ju\vert^p_j u^θ=f · amp; \hboxin Ω,
u · gt;0 · amp; \hboxin Ω, u =0 · amp; \hboxon ∂Ω, . Ω is a bounded domain in ℝ^N, j∈ J=\1,2,…,N\, q>0, 0< θ<1, 2≤ p₁≤ p₂≤... ≤ p_N and f∈ L¹(Ω). Our study's conclusions will depend on the values of q and θ.

Citations

• Anisotropic elliptic equations involving unbounded coefficients and singular nonlinearities
• Singular anisotropic elliptic equations with gradient-dependent lower order terms
• Anisotropic elliptic equations with gradient-dependent lower order terms and L¹ data
• Existence and nonexistence of solutions for singular quadratic quasilinear equations

Related

• Anisotropic elliptic equations involving unbounded coefficients and singular nonlinearities
• Sharp estimates and existence for anisotropic elliptic problems with general growth in the gradient
• Singular anisotropic elliptic equations with gradient-dependent lower order terms
• Anisotropic elliptic equations with gradient-dependent lower order terms and L¹ data
• Boundedness of solutions to singular anisotropic elliptic equations