Self-adjoint extensions of the Laplace–Beltrami operator and unitaries at the boundary

@article{Ibort2015SelfadjointEO,
  title={Self-adjoint extensions of the Laplace–Beltrami operator and unitaries at the boundary},
  author={Alberto Ibort and F. Lled{\'o} and J. M. P'erez-Pardo},
  journal={Journal of Functional Analysis},
  year={2015},
  volume={268},
  pages={634-670}
}
Abstract We construct in this article a class of closed semi-bounded quadratic forms on the space of square integrable functions over a smooth Riemannian manifold with smooth compact boundary. Each of these quadratic forms specifies a semi-bounded self-adjoint extension of the Laplace–Beltrami operator. These quadratic forms are based on the Lagrange boundary form on the manifold and a family of domains parametrized by a suitable class of unitary operators on the boundary that will be called… Expand
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