José Miguel Urbano

Qualitative-to-quantitative regularity for degenerate equations

We establish a principle that converts qualitative regularity into uniform interior estimates for degenerate equations. For the $p$-Laplace equation, $p>2$, we prove that local $C^{1,\gamma}$ regularity of every solution, without any uniform bound on the corresponding seminorms, implies uniform $C^{1,\beta}$ estimates...