J. Behrndt and M. Langer,
Boundary value problems for elliptic partial differential operators on bounded domains,
J. Funct. Anal. 243 (2007), 536–565
Abstract:
For a symmetric operator or relation A with infinite deficiency indices in a
Hilbert space we develop an abstract framework for the description of symmetric and
self-adjoint extensions AΘ of A as
restrictions of an operator or relation T which is a core of the
adjoint A∗.
This concept is applied to second order elliptic partial differential operators on
smooth bounded domains, and a class of elliptic problems with eigenvalue dependent
boundary conditions is investigated.