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.
Original language | English (US) |
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Pages (from-to) | 6481-6495 |
Number of pages | 15 |
Journal | International Mathematics Research Notices |
Volume | 2018 |
Issue number | 20 |
DOIs | |
State | Published - Oct 23 2018 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics