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https://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 | Serial title, monograph or event: | International Mathematics Research Notices | 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: | https://hdl.handle.net/10316/44406 | DOI: | 10.1093/imrn/rnx068 10.1093/imrn/rnx068 |
Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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Urbano_paper11.pdf | 304.22 kB | Adobe PDF | View/Open |
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