Remarks on functions with bounded Laplacian

2016/05/17 by Tarek M. Elgindi, Elgindi, Tarek M. · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1605.05266

openalex publication_date 2016/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Δψ:=(∂² ψ)/(∂ x₁²)+(∂² ψ)/(∂ x₂²) being locally bounded does not imply that D²ψ is locally bounded. However, we prove that if ψ is invariant under rotation by (2π)/(m), for some m≥ 3, and Δψ is locally bounded, then sup_{x∈ B1(0)}(|∇ ψ(x)|)/(|x|)

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