a1 Mathematisches Institut der Universität Bismarckstraße 1 1/2 D-8520 Erlangen Federal Republic of Germany
For a class of formally hypoelliptic differential operators in divergence form we prove a generalized Gårding 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.
(Received March 03 1986)
(Revised November 04 1986)
1980 Mathematics subject classification (Amer. Math. Soc.)