Pointwise gradient estimates for a class of singular quasilinear\n equation with measure data

2019/02/12 by Quoc‐Hung Nguyen, Nguyen, Quoc-Hung, Nguyen Cong Phuc +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1902.04414

openalex publication_date 2019/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Local and global pointwise gradient estimates are obtained for solutions to\nthe quasilinear elliptic equation with measure data\n-÷(A(x,\∇ u))=\μ in a bounded and possibly nonsmooth\ndomain \Ω in \ℝⁿ. Here ÷(A(x,\∇ u)) is\nmodeled after the p-Laplacian. Our results extend earlier known results to\nthe singular case in which \(3n-2)/(2n-1)<p\≤ 2-\(1)/(n).\n

Citations

• Solution of the Plateau problem for m-dimensional surfaces of varying topological type

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• Gradient continuity estimates for elliptic equations of singular p-Laplace type with measure data

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