J Austral Math Soc Ser A 44 pp324--349, 1988.

On Dirichlet's Boundary Value Problem for Some Formally Hypoelliptic Differential Operators

Niels Jacob

(Received 3 March 1986; revised 4 November 1986)

Abstract

For a class of formally hypoellipctic differential operators in divergence form we prove a generalized Garding 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.

1980 AMS Subject Classification: 35G15, 35H05

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Authors

Niels Jacob: Mathematisches Instutut der Universität, Bismarckstraße 1 1/2, D-8520 Erlangen, Federal Republic of Germany.

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Last Modified: Wed Feb 19 10:27:48 2003