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

Part of:General higher-order equations and systems

Published online by Cambridge University Press:  09 April 2009

Niels Jacob
Niels Jacob
Affiliation:
Mathematisches Institut der UniversitätBismarckstraße 1 1/2 D-8520 Erlangen Federal Republic of Germany
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Abstract

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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.

MSC classification

Secondary:35G15: Boundary value problems for linear higher-order equations

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 3 , June 1988, pp. 324 - 349
Copyright
Copyright © Australian Mathematical Society 1988

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