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 Cp′=C1, [Formula presented] this regularity is optimal.
|Original language||English (US)|
|Number of pages||13|
|Journal||Advances in Mathematics|
|State||Published - Aug 20 2017|
Bibliographical noteGenerated from Scopus record by KAUST IRTS on 2023-02-15
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