BMO SOLUTIONS TO QUASILINEAR EQUATIONS OF p-LAPLACE TYPE

Document Type

Article

Publication Date

1-1-2022

Abstract

We give necessary and sufficient conditions for the existence of a BMO solution to the quasilinear equation −∆pu = µ in ℝn, u ≥ 0, where µ is a locally finite Radon measure, and ∆pu = div(|∇u|p−2∇u) is the p-Laplacian (p > 1). We also characterize BMO solutions to equations −∆pu = σuq + 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 div(A(x, ∇·)) in place of ∆p

Publication Source (Journal or Book title)

Annales De L Institut Fourier

First Page

1911

Last Page

1939

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