Towards the Cp′-Regularity Conjecture in Higher Dimensions

Damião J. Araújo, Eduardo V. Teixeira, José Miguel Urbano

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)6481-6495
Number of pages15
JournalInternational Mathematics Research Notices
Issue number20
StatePublished - Oct 23 2018
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

  • General Mathematics


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