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

In this paper we establish Schauder estimates for the sublalpace equation $Σ_{j = 1}^mX_j^2u = f,$ where ${X_1},{X_2}, \ldots ,{X_m}$ 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.

No reviews yet.

No comments yet.