Boundary value problems for elliptic partial differential operators on bounded domains

Jussi Behrndt, M. Langer

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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.
Original languageEnglish
Pages (from-to)536-565
Number of pages30
JournalJournal of Functional Analysis
Volume243
Issue number2
DOIs
Publication statusPublished - 15 Feb 2007

Keywords

  • boundary triple
  • self-adjoint extension
  • weyl function
  • M-operator
  • Dirichlet-to-Neumann map
  • Krein's formula
  • elliptic differential operator
  • boundary value problem

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