BMO solutions to quasilinear equations of p-Laplace type

2021/05/11 by Nguyen Cong Phuc, Phuc, Nguyen Cong, Igor E. Verbitsky +1
Computer Science · Mathematics · #2010: Primary 35J92 #42B35 42B35 #42B37 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Secondary 31B15 #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2105.05282

openalex publication_date 2021/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give necessary and sufficient conditions for the existence of a BMO solution to the quasilinear equation -Δ_p u = μ in ℝⁿ, u≥ 0, where μ is a locally finite Radon measure, and Δ_pu= div(|∇ u|^p-2∇ u) is the p-Laplacian (p>1). We also characterize BMO solutions to equations -Δ_p u = σu^q + μ in ℝⁿ, u≥ 0, with q>0, where both μ and σ are locally finite Radon measures. Our main results hold for a class of more general quasilinear operators \rm div(A(x, ∇ ⋅)) in place of Δ_p.

Related

• p-Laplacian type equations involving measures
• Remarks on some quasilinear equations with gradient terms and measure data
• Existence problems for the p-Laplacian
• Potential estimates and quasilinear parabolic equations with measure data
• Uniqueness of entire solutions to quasilinear equations of p-Laplace type