Publication date:
20 August 2017
Source:Advances in Mathematics, Volume 316
Author(s): Damião J. Araújo, Eduardo V. Teixeira, José Miguel Urbano
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 $C^{p^{\prime }}=C^{1,\frac{1}{p-1}}$; this regularity is optimal.