A proof of the $C^{p^\prime}$-regularity conjecture in the plane
Analysis of PDEs
2020-01-03 v1
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 -Poisson equation with a bounded source are locally of class ; this regularity is optimal.
Cite
@article{arxiv.1901.03827,
title = {A proof of the $C^{p^\prime}$-regularity conjecture in the plane},
author = {Damião J. Araújo and Eduardo V. Teixeira and José Miguel Urbano},
journal= {arXiv preprint arXiv:1901.03827},
year = {2020}
}
Comments
The proof of Theorem 6 has been slightly amended with respect to the published version; some minor typos were also corrected