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The dirichlet problem for sub-elliptic second order equations
Authors:Alberto Parmeggiani  Chao-Jiang Xu
Institution:(1) Present address: Department of Mathematics, University of Bologna, P.za di Porta S. Donate, 40127 Bologna, Italy;(2) Present address: Institute of Mathematics, Wuhan University, 430072 Wuhan, China
Abstract:The Cinfin-regularity up to the boundary of solutions to the Dirichlet problem: 
$$Lu =   = f \in C^\infty  (\bar \Omega ), u _{|\partial \Omega }  = g \in C^\infty  (\partial \Omega )$$
is proved, using a comparison principle of L with a Hörmander's type operator sum X j * Xj, where OHgr is a smooth bounded open subset of Rn, and 
$$L =   - \sum\limits_{i,j} {\partial _i (a_{ij} (x)\partial _j ) + c(x)} $$
is a second-order degenerate elliptic operator with smooth coefficients, satisfying the so-called Fefferman-Phong's condition.
Keywords:
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