Schauder estimates for solutions of sub-Laplace equations with Dini terms

Abstract

In this paper we establish Schauder estimates for the sublalpace equation \[Σ_{j = 1}^mX_j^2u = f,\] where $X_1,X_2,\dots ,X_m$ is a system of smooth vector field which generates the first layer in the Lie algebra of a Carnot group. We drive the estimate for the second order derivatives of the solution to the equation with Dini continue inhomogeneous term $f$ by the perturbation argument.

arXiv comment12 pages