Anisotropic elliptic equations involving unbounded coefficients and singular nonlinearities

2025/11/29 by Fessel Achhoud, achhoud, Fessel, Hichem Khelifi +1 · 1 citation
Mathematics · #Nonlinear Partial Differential Equations #Nonlinear Differential Equations Analysis #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.2512.00485

Abstract

In this paper, we study the existence and regularity of solutions for a class of nonlinear singular elliptic equations involving unbounded coefficients and a singular right-hand side. Specifically, we are interested to problem whose simplest model is -∑_j=1^N∂_j([1+u^q]\vert ∂_j u \vert^p_j-2 ∂_j u)= (f)/(u^γ) in D, ugt;0 in D, u=0 \hbox on \partialD, where D is a bounded open subset of ℝ^N with N>2, γ≥0, q >0 , p_j>2 for all j=1,...,N and the source term f belongs to L¹(D), with f ≥ 0 and f \not≡ 0.

Citations

• Fully anisotropic elliptic problems with minimally integrable data
• Comparison results for nonlinear anisotropic parabolic problems

Cited by

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

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