Title
A Proof Of The CP′-Regularity Conjecture In The Plane
Keywords
Nonlinear pdes; Regularity theory; Sharp estimates
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 Cp′=C1, [Formula presented] this regularity is optimal.
Publication Date
8-20-2017
Publication Title
Advances in Mathematics
Volume
316
Number of Pages
541-553
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1016/j.aim.2017.06.027
Copyright Status
Unknown
Socpus ID
85021291481 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/85021291481
STARS Citation
Araújo, Damião J.; Teixeira, Eduardo V.; and Urbano, José Miguel, "A Proof Of The CP′-Regularity Conjecture In The Plane" (2017). Scopus Export 2015-2019. 5988.
https://stars.library.ucf.edu/scopus2015/5988