jRegularity for QuasilinearSecond Order Subelliptic Equations i CHAO JIANG XU
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20
pages
English
Documents
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jRegularity for QuasilinearSecond-Order Subelliptic Equations i ' CHAO-JIANG XU Courant lnstitute and i ~ Wuhan University 1 ~ , Abstract ln this paper, we study the regularity of solutions of the quasilinear equation 1 m LAjj(x,u,xu)XjXjU +B(x,u,Xu) = 0 jj=i where X = (Xi,...,Xm) is a system of real smooth vector fields, Ajj,B E COO(O x Rm+l). Assume that X satisfies the Hôrmander condition and (Ajj(x, z,ç)) is positive definite. We prove that if u E s2,a(o) (see Section 2) is a solution of the above equation, then u E COO(O). .. Introduction 1~ ln this work, we study the regularity of solutions of the following quasi- i linear second-order degenerate elliptic equation: m (*) LAij(X,U,XU)XiXju+B(x,u,Xu) =0 ij=1 where X = (X1,...,Xm) is a system of real smooth vector fields defined in an open domain M of Rn, n ~ 3, and Aij,B E C(.Q x Rm+I), i,j = l,..., m.
Voir
- can differentiate
- quasilinear subelliptic
- differential operator
- sec- tion
- hôrmander condition
- distance p3
- chao-jiang xu
- small compact
- linearly independent
- vxo'
