A Proof Of The C^P′-Regularity Conjecture In The Plane

Creator

Damião J. Araújo, Universidade Federal da Paraíba
Eduardo V. Teixeira, University of Central Florida
José Miguel Urbano, University of Coimbra, Centre for Mathematics

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 C^P′-Regularity Conjecture In The Plane" (2017). Scopus Export 2015-2019. 5988.
https://stars.library.ucf.edu/scopus2015/5988