Year: 2016
Type: preprint
Abstract: We prove a $\mathsf{C}^1$-elliptic estimate of the form $ \sup_{B(x,r/2)} |\mathrm{grad} (ψ) | \leq C \left\{ \sup_{B(x,r)} |Δψ| + \sup_{B(x,r)} |ψ| \right\}, $ valid on any complete Riemannian manifold $M$ and for any smooth function $ψ$ which is defined in a nighbourhood of $B(x,r)$, with an explicit quantitative control on the constant $C=C(B(x,r))$ in terms of the curvature of the geodesic ball $B(x,r)\subset M$.
Source: arXiv (Cornell University)
Authors: Güneysu, Batu, Pigola, Stefano
Institution: University of Insubria
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4300001504