A proof of the Cp′-regularity conjecture in the plane

Damião J. Araújo, Eduardo V. Teixeira, José Miguel Urbano

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


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 languageEnglish (US)
Pages (from-to)541-553
Number of pages13
JournalAdvances in Mathematics
StatePublished - Aug 20 2017
Externally publishedYes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

  • General Mathematics


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