کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4590292 | 1334945 | 2015 | 37 صفحه PDF | دانلود رایگان |
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 admissible. The corresponding quadratic forms are semi-bounded below and closable. Finally, the representing operators correspond to semi-bounded self-adjoint extensions of the Laplace–Beltrami operator. This family of extensions is compared with results existing in the literature and various examples and applications are discussed.
Journal: Journal of Functional Analysis - Volume 268, Issue 3, 1 February 2015, Pages 634–670