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

Dominic Breit, Andrea Cianchi, Lars Diening, Tuomo Kuusi, S. Schwarzacher

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)200-212
Number of pages13
JournalNonlinear Analysis: Theory, Methods and Applications
Volume153
Early online date10 Aug 2016
DOIs
Publication statusPublished - Apr 2017

Keywords

  • Elliptic systems
  • Gradient regularity
  • Sharp maximal operator

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'The p-Laplace system with right-hand side in divergence form: Inner and up to the boundary pointwise estimates'. Together they form a unique fingerprint.

  • Cite this