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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 C-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 X _j ^* X_j, where 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.

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