On Dirichlet's boundary value problem for some formally hypoelliptic differntial operators

Niels Jacob
1988 Journal of the Australian Mathematical Society  
For a class of formally hypoelliptic differential operators in divergence form we prove a generalized Girding inequality. Using this inequality and further properties of the sesquilinear form generated by the differential operator a generalized homogeneous Dirichlet problem is treated in a suitable Hilbert space. In particular Fredholm's alternative theorem is proved to be valid.
doi:10.1017/s1446788700032134 fatcat:bwgyfidkevh4vcmbant7w25hte