Towards the Cp′-Regularity Conjecture in Higher Dimensions

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

doi:10.1093/imrn/rnx068

Towards the Cp′-Regularity Conjecture in Higher Dimensions

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

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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)
Pages (from-to)	6481-6495
Number of pages	15
Journal	International Mathematics Research Notices
Volume	2018
Issue number	20
DOIs	https://doi.org/10.1093/imrn/rnx068
State	Published - Oct 23 2018
Externally published	Yes

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

ASJC Scopus subject areas

General Mathematics

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10.1093/imrn/rnx068

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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.",

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AU - Araújo, Damião J.

AU - Teixeira, Eduardo V.

AU - Urbano, José Miguel

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PY - 2018/10/23

Y1 - 2018/10/23

N2 - 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.

AB - 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.

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JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 20

ER -

Towards the Cp′-Regularity Conjecture in Higher Dimensions

Abstract

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