no. 5
BMO solutions to quasilinear equations of p-Laplace type
Phuc, Nguyen Cong1; Verbitsky, Igor E.2
1 Department of Mathematics, Louisiana State University, 303 Lockett Hall, Baton Rouge, LA 70803 (USA)
2 Department of Mathematics, University of Missouri, Columbia, MO 65211 (USA)
Annales de l'Institut Fourier, Volume 72 (2022) no. 5, pp. 1911-1939.

We give necessary and sufficient conditions for the existence of a BMO solution to the quasilinear equation -Δ p u=μ in ℝ n , u≥0, where μ is a locally finite Radon measure, and Δ p u=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 ℝ n , 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 Δ p .

Nous donnons les conditions nécessaires et suffisantes pour l’existence d’une solution BMO de l’équation quasi-linéaire -Δ p u=μ dans ℝ n , u≥0, où μ est une mesure de Radon localement finie, et Δ p u=div(|∇u| p-2 ∇u) est le p-Laplacien (p>1).

Nous caractérisons également les solutions BMO de l’équation -Δ p u=σu q +μ dans ℝ n , u≥0, avec q>0, où μ et σ sont des mesures de Radon localement finies. Nos principaux résultats sont valables pour la classe plus générale des opérateurs quasi-linéaires plus généraux div(𝒜(x,∇·)) à la place de Δ p .

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3485
Classification: 35J92, 42B37, 31B15, 42B35
Keywords: BMO spaces, Wolff potentials, $p$-Laplacian
Mot clés : Espaces BMO, potentiels de Wolff, $p$-Laplacien
Phuc, Nguyen Cong 1; Verbitsky, Igor E. 2

1 Department of Mathematics, Louisiana State University, 303 Lockett Hall, Baton Rouge, LA 70803 (USA)
2 Department of Mathematics, University of Missouri, Columbia, MO 65211 (USA)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Phuc, Nguyen Cong; Verbitsky, Igor E. BMO solutions to quasilinear equations of $p$-Laplace type. Annales de l'Institut Fourier, Volume 72 (2022) no. 5, pp. 1911-1939. doi : 10.5802/aif.3485. https://aif.centre-mersenne.org/articles/10.5802/aif.3485/

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