The Friedrichs Extension of Elliptic Operators with Conditions on Submanifolds of Arbitrary Dimension

Anton Savin ()
Additional contact information
Anton Savin: Nikolskii Mathematical Institute, RUDN University, Miklukho-Maklaya Str. 6, 117198 Moscow, Russia

Mathematics, 2024, vol. 12, issue 3, 1-9

Abstract: We describe the Friedrichs extension of elliptic symmetric pseudodifferential operators on a closed smooth manifold with the domain consisting of functions vanishing on a given submanifold. In summary, the Friedrichs extension is an elliptic Sobolev problem defined in terms of boundary and coboundary operators, and the number of boundary and coboundary conditions in the problem depends on the order of the operator and the codimension of the submanifold. In this paper, the discreteness of the spectrum is proved, and singularities of eigenfunctions are described.

Keywords: Friedrichs extension; Sobolev problems; boundary conditions on submanifolds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/3/418/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/3/418/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:3:p:418-:d:1327752

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().