Continuity properties of solutions to the p-Laplace system-Reference-Cited by-同舟云学术

Continuity properties of solutions to the p-Laplace system

Published:2017-01-01 Issue:1 Volume:10 Page:1-24
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
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Author:

Alberico Angela¹,Cianchi Andrea²,Sbordone Carlo³

Affiliation:

1. 1Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Sezione di Napoli, Via P. Castellino 111, 80131 Napoli, Italy

2. 2Dipartimento di Matematica e Informatica “U. Dini”, Università degli Studi di Firenze, Piazza Ghiberti 27, 50122 Firenze, Italy

3. 3Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Via Cintia, 80126 Napoli, Italy

Abstract

AbstractA sharp integrability condition on the right-hand side of the p-Laplace system for all its solutions to be continuous is exhibited. Their uniform continuity is also analyzed and estimates for their modulus of continuity are provided. The relevant estimates are shown to be optimal as the right-hand side ranges in classes of rearrangement-invariant spaces, such as Lebesgue, Lorentz, Lorentz–Zygmund, and Marcinkiewicz spaces, as well as some customary Orlicz spaces.

Funder

MIUR

GNAMPA

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2015-0029/pdf

Reference62 articles.

1. On embeddings between classical Lorentz spaces;Math. Inequal. Appl.,2001

2. On maximal functions in Orlicz spaces;Proc. Amer. Math. Soc.,1996