Title
Towards The CP′-Regularity Conjecture In Higher Dimensions
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 CP′-Regularity Conjecture In Higher Dimensions" (2018). Scopus Export 2015-2019. 10002.
https://stars.library.ucf.edu/scopus2015/10002