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 
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: http://hdl.handle.net/10316/44401
Other Identifiers: 10.1016/j.aim.2017.06.027
DOI: 10.1016/j.aim.2017.06.027
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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