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Schauder estimates for solutions of sub-Laplace equations with Dini terms (1402.7120v1)
Published 28 Feb 2014 in math.AP
Abstract: In this paper we establish Schauder estimates for the sublalpace equation [\Sigma_{j = 1}mX_j2u = 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.