Second Step Carnot Group Subelliptic Equations Schauder Estimate

The theory of Schauder estimates for sub-elliptic equations is still in a developing status, especially for the global case (boundary value problems). In this thesis we mainly study Schauder estimates for second order sub-elliptic partial equations in Carnot groups of step 2.We establish Schauder estimates of second derivatives for a class of sub-elliptic equations in R" of the kind where X1,…,X1 are left invariant vector fields of step two Carnot groups G=(Rn,ο,δλ). X1,…,X1 are left invariant vector fields which generate the first layer of the Lie algebra of G. The main tools used in this thesis are the Taylor formula for CH2 functions on G and some properties of the corresponding Taylor polynomials.The thesis extends some results in Gutierrez and Lanconelli to the CH2 case.