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Boundary value problems for elliptic partial differential operators on bounded domains

Behrndt, Jussi and Langer, M. (2007) Boundary value problems for elliptic partial differential operators on bounded domains. Journal of Functional Analysis, 243 (2). pp. 536-565. ISSN 0022-1236

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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 A_Θ 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.