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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
|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.|
|Appears in Collections:||I&D CMUC - Artigos em Revistas Internacionais|
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