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If you have a second order elliptic equation but the coefficients of the second order terms only form a nonnegative (instead of positive definite) matrix, then, do you know if there is any literature about this? (For example, the matrix of the second order terms can be diag{1,1,0,0} )

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do you mean positive semi-definite –  tergi Jul 11 '12 at 16:05
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closed as off-topic by Ricardo Andrade, Theo Johnson-Freyd, Andrey Rekalo, Willie Wong, Stefan Kohl Nov 27 '13 at 11:01

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