BMO estimates for the \(p\)-Laplacian
type: Item
instance of: scholarly article
title: BMO estimates for the \(p\)-Laplacian
zbMATH Open document ID: 1233.35056
author: Lars Diening
author: P. Kaplický
author: S. Schwarzacher
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2011-12-08T00:00:00Z
review text: The authors prove BMO estimates of the inhomogeneous \(p\)-Laplace system \[ -\text{div }(|\nabla u|^{p-2}\nabla u)=\text{div }f,\qquad p\in(1,\infty). \] It is shown that \(f\in\) BMO implies \(|\nabla u|^{p-2}\nabla u\in\) BMO, which is the limiting case of the nonlinear Calderón-Zygmund theory. Moreover, it is proved that \(A(\nabla u)=\varphi'(|\nabla u|)\frac{\nabla u}{|\nabla u|}\) inherits the Campanato and VMO regularity of \(f.\)
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J92
Mathematics Subject Classification ID: 35J47
zbMATH DE Number: 5987796
zbMATH Keywords: elliptic systems
zbMATH Keywords: \(p\)-Laplace
zbMATH Keywords: BMO estimates
zbMATH Keywords: nonlinear Calderón-Zygmund theory
zbMATH Keywords: Campanato estimates
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: j.na.2011.08.065
OpenAlex ID: W2112668064
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DOI: 10.1016/J.NA.2011.08.065
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description: scientific article; zbMATH DE number 5987796