Quantitative C^1 - estimates on manifolds

Batu Güneysu, Stefano Pigola

We prove a ${\mathsf{C}}^1$-elliptic estimate of the form ${\sup }_{B(x,r/2)}|\mathrm{grad}(\psi )|\le C\left\{{\sup }_{B(x,r)}|\Delta \psi |+{\sup }_{B(x,r)}|\psi |\right\},$ valid on any comple…