Universal potential estimates for 1 < p ≤ 2 - 1n y

Document Type

Article

Publication Date

1-1-2023

Abstract

We extend the so-called universal potential estimates of Kuusi-Mingione type (J. Funct. Anal. 262: 4205-4269, 2012) to the singular case 1 < p ≤ 2 - 1=n for the quasilinear equation with measure data ( equation presented) in a bounded open subset Ω of Rn, n ≥ 2, with a finite signed measure μ in Ω. The operator div(A(x; ∇u)) is modeled after the p-Laplacian Δpu := div (j∇ujp-2∇u), where the nonlinearity A(x; Ξ) (x; Ξϵ Rn) is assumed to satisfy natural growth and monotonicity conditions of order p, as well as certain additional regularity conditions in the x-variable.

Publication Source (Journal or Book title)

Mathematics in Engineering

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