For question involving Hilbert spaces, that is, complete normed spaces whose norm comes from an inner product.

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When is the Laplace Beltrami Operator self-adjoint?

The Laplace-Beltrami operator is an operator which is the typical example of a self-adjoint operator in $L^{2}$. I am wondering if this is also true for other Hilbert spaces $W^{k,2}$. If this is ...