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https://hdl.handle.net/10316/44401
Title: | A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the plane | Authors: | Araújo, Damião J. Teixeira, Eduardo V. Urbano, José Miguel |
Issue Date: | 2017 | Publisher: | Elsevier | Project: | info:eu-repo/grantAgreement/FCT/5876/147205/PT | Serial title, monograph or event: | Advances in Mathematics | Volume: | 316 | Abstract: | We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are able to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class C^p'=C^(1,1/(p-1)) ; this regularity is optimal. | URI: | https://hdl.handle.net/10316/44401 | DOI: | 10.1016/j.aim.2017.06.027 10.1016/j.aim.2017.06.027 |
Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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Urbano_paper9.pdf | 286.65 kB | Adobe PDF | View/Open |
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