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

2014/02/28 by Tingxi Hu, Hu, Tingxi, Pengcheng Niu +1
Mathematics · #35B65 #35R03 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B65 #msc:35R03

paper · pdf · doi:10.48550/arxiv.1402.7120

12 pages

arxiv created 2014/02/28 · arxiv updated 2014/03/03

Abstract

In this paper we establish Schauder estimates for the sublalpace equation Σ_{j = 1}^mX_j²u = f, where X₁,X₂, … ,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.

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