On Neumann-Poincaré operators and self-adjoint transmission problems

Publikationstyp
Journal Article
Date Issued
2025-09-29
Sprache
English
Author(s)
Benhellal, Badreddine 
Mathematik E-10  
Pankrashkin, Konstantin  
TORE-URI
https://hdl.handle.net/11420/58047
Journal
Revista matemática complutense  
Citation
Revista Matematica Complutense (in Press): (2025)
Publisher DOI
10.1007/s13163-025-00544-6
Scopus ID
2-s2.0-105017383685
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