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On Neumann-Poincaré operators and self-adjoint transmission problems
Publikationstyp
Journal Article
Date Issued
2025-09-29
Sprache
English
Journal
Volume
39
Issue
2
Start Page
407
End Page
430
Citation
Revista Matematica Complutense 39 (2): 407 -430 (2025)
Publisher DOI
Scopus ID
Publisher
Springer
We discuss the self-adjointness in L2-setting of the operators acting as -∇·h∇, with piecewise constant functions h having a jump along a Lipschitz hypersurface Σ, without explicit assumptions on the sign of h. We establish a number of sufficient conditions for the self-adjointness of the operator with Hs-regularity for suitable s∈[1,32], in terms of the jump value and the regularity and geometric properties of Σ. An important intermediate step is a link with Fredholm properties of the Neumann-Poincaré operator on Σ, which is new for the Lipschitz setting.
Subjects
Fredholm theory
Neumann-Poincaré operators
Self-adjointness
Transmission problems
DDC Class
510: Mathematics