Pointwise Calderon-Zygmund gradient estimates for the p-Laplace system
| Autor(en): | Breit, Dominic Cianchi, Andrea Diening, Lars Kuusi, Tuomo Schwarzacher, Sebastian |
Stichwörter: | BOUNDS; Campanato spaces; EQUATIONS; FUNCTIONALS; Gradient regularity; INEQUALITIES; INTEGRABILITY; Mathematics; Mathematics, Applied; MINIMIZERS; Nonlinear elliptic systems; NONLINEAR ELLIPTIC-SYSTEMS; Rearrangement-invariant spaces; REGULARITY; Sharp maximal function | Erscheinungsdatum: | 2018 | Herausgeber: | ELSEVIER SCIENCE BV | Enthalten in: | JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | Band: | 114 | Startseite: | 146 | Seitenende: | 190 | Zusammenfassung: | Pointwise estimates for the gradient of solutions to the p-Laplace system with righthand side in divergence form are established. Their formulation involves the sharp maximal operator, whose properties enable us to develop a nonlinear counterpart of the classical Calderon-Zygmund theory for the Laplacian. As a consequence, a flexible, comprehensive approach to gradient bounds for the p-Laplace system for a broad class of norms is derived. The relevant gradient bounds are just reduced to norm inequalities for a classical operator of harmonic analysis. In particular, new gradient estimates are exhibited which augment the available literature in the elliptic regularity theory. (C) 2017 Elsevier Masson SAS. All rights reserved. |
ISSN: | 00217824 | DOI: | 10.1016/j.matpur.2017.07.011 |
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