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THE BOUNDARY CONDITIONS DESCRIPTION OF TYPE I DOMAINS

Published online by Cambridge University Press:  25 August 2010

MOHAMED EL-GEBEILY  and
DONAL O'REGAN
MOHAMED EL-GEBEILY
Affiliation:
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia e-mail: mgebeily@kfupm.edu.sa
DONAL O'REGAN
Affiliation:
Department of Mathematics, National University of Ireland, University Road, Galway, Ireland
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Abstract

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Type I domains are the domains of the self-adjoint operators determined by the weak formulation of formally self-adjoint differential expressions ℓ. This class of operators is defined by the requirement that the sesquilinear form q(u, v) obtained from ℓ by integration by parts agrees with the inner product 〈ℓu, v〉. A complete characterisation of the boundary conditions assumed by functions in these domains for second-order differential expressions is given in this paper. In the singular case, the boundary conditions are stated in terms of certain ‘boundary condition’ functions and in the regular case they are given in terms of classical function values.

Keywords

34B1534A34

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 619 - 633
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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