Towards The C^P′-Regularity Conjecture In Higher Dimensions

Creator

Damião J. Araújo, Universidade Federal da Paraíba
Eduardo V. Teixeira, University of Central Florida
José Miguel Urbano, University of Coimbra, Centre for Mathematics

Abstract

A longstanding conjecture in elliptic regularity theory inquires whether a W1,p function whose p-laplacian is bounded is locally of class C1, 1/p-1. While it is well known that such functions are of class C1,α for some unknown 0 ≤ α ≤ 1, establishing the sharp estimate turns out to be a rather delicate problem. Quite recently, the authors managed to establish the conjecture in the plane. In this article, we address the conjecture in higher dimensions and confirm its validity in a number of other meaningful cases.

Publication Date

10-23-2018

Publication Title

International Mathematics Research Notices

Volume

2018

Issue

20

Number of Pages

6481-6495

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1093/imrn/rnx068

Copyright Status

Unknown

Socpus ID

85044547633 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85044547633

STARS Citation

Araújo, Damião J.; Teixeira, Eduardo V.; and Urbano, José Miguel, "Towards The C^P′-Regularity Conjecture In Higher Dimensions" (2018). Scopus Export 2015-2019. 10002.
https://stars.library.ucf.edu/scopus2015/10002