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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
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.
Peer review: yes
DOI: 10.1016/j.aim.2017.06.027
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Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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