BMO estimates for the p-Laplacian

被引：67

作者：

Diening, L. ^{[1
]}

Kaplicky, P. ^{[2
]}

Schwarzacher, S. ^{[1
]}

机构：

[1] Ludwig Maximilians Univ Munchen, Inst Math, D-80333 Munich, Germany

[2] Charles Univ Prague, Prague 8, Czech Republic

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2012年 / 75卷 / 02期

关键词：

Elliptic systems; BMO estimates; Nonlinear Calderon-Zygmund theory; Campanato estimates; ELLIPTIC-SYSTEMS; REGULARITY; GRADIENT;

D O I：

10.1016/j.na.2011.08.065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove BMO estimates of the inhomogeneous p-Laplace system given by -div (|del u|(p) (2) del u) = div f. We show that f is an element of BMO implies |del u|(p-2)del u is an element of BMO, which is the limiting case of the nonlinear Calderon-Zygmund theory. This extends the work of DiBenedetto and Manfredi (1993) [2], which was restricted to the super-quadratic case p >= 2, to the full case 1 < p < infinity and even more general growth. Moreover, we prove that A(del u) inherits the Campanato and VMO regularity of f. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：637 / 650

页数：14

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