Journal of the Australian Mathematical Society (Series A)

Table of Contents - 1988 - Volume 44, Issue 03  

Research Article

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

Niels Jacoba1

a1 Mathematisches Institut der Universität Bismarckstraße 1 1/2 D-8520 Erlangen Federal Republic of Germany

Abstract

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.)

  • 35 G 15;
  • 35 H 05