The p-Laplace system with right-hand side in divergence form: Inner and up to the boundary pointwise estimates

被引：19

作者：

Breit, D. ^{[1
]}

Cianchi, A. ^{[2
]}

Diening, L. ^{[3
]}

Kuusi, T. ^{[4
]}

Schwarzacher, S. ^{[5
]}

机构：

[1] Heriot Watt Univ, Sch Math & Comp Sci, Edinburgh EH14 4AS, Midlothian, Scotland

[2] Univ Florence, Dipartimento Matemat & Informat U Dini, Viale Morgagni 67-A, I-50134 Florence, Italy

[3] Univ Osnabruck, Inst Math, Albrechtstr 28a, D-49076 Osnabruck, Germany

[4] Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland

[5] Charles Univ Prague, Fac Math & Phys, Dept Math Anal, Sokolovska 83, Prague, Czech Republic

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2017年 / 153卷

基金：

芬兰科学院;

关键词：

Elliptic systems; Gradient regularity; Sharp maximal operator; NONLINEAR ELLIPTIC-SYSTEMS; REGULARITY; GRADIENT; FUNCTIONALS; POTENTIALS; MINIMIZERS; EQUATIONS;

D O I：

10.1016/j.na.2016.06.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note we collect some very recent pointwise bounds for the gradient of solutions, and for the solutions themselves, to the p-Laplace system with right-hand side in divergence form. Both estimates inside the domain for local solutions, and global estimates for solutions to boundary value problems are discussed. Their formulation involves sharp maximal operators, whose properties enable us to translate some aspects of the elliptic regularity theory into a merely harmonic analytic framework. As a consequence, a flexible, comprehensive approach to estimates for solutions to the p-Laplace system for a broad class of norms is derived. In particular, global estimates under minimal boundary regularity are presented.

引用

页码：200 / 212

页数：13