Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-adjoint curl operators   We study the exterior derivative as a symmetric unbounded operator on square
integrable 1-forms on a 3D bounded domain $D$. We aim to identify boundary
conditions that render this operator self-adjoint. By the symplectic version of
the Glazman-Krein-Naimark theorem this amounts to identifying complete
Lagrangian subspaces of the trace space of H(curl) equipped with a symplectic
pairing arising from the $\wedge$-product of 1-forms on $\partial D$.
Substantially generalizing earlier results, we characterize Lagrangian
subspaces associated with closed and co-closed traces. In the case of
non-trivial topology of the domain, different contributions from co-homology
spaces also distinguish different self-adjoint extension. Finally, all
self-adjoint extensions discussed in the paper are shown to possess a discrete
point spectrum, and their relationship with curl curl-operators is discussed.

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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int