Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/44406
 Title: Towards the $C^{p^\prime}$-Regularity Conjecture in Higher Dimensions Authors: Araújo, Damião J. Teixeira, Eduardo V. Urbano, José Miguel Issue Date: 2017 Publisher: Oxford University Press Project: info:eu-repo/grantAgreement/FCT/5876/147205/PT Abstract: A longstanding conjecture in elliptic regularity theory inquires whether a W^{1,p} function whose p-laplacian is bounded is locally of class C^{1,\frac{1}{p-1}}. While it is well known that such functions are of class C^{1,\alpha} 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. URI: http://hdl.handle.net/10316/44406 Other Identifiers: 10.1093/imrn/rnx068 DOI: 10.1093/imrn/rnx068 Rights: embargoedAccess Appears in Collections: I&D CMUC - Artigos em Revistas Internacionais

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