TY - JOUR
T1 - Boundary integral formulations of eigenvalue problems for elliptic differential operators with singular interactions and their numerical approximation by boundary element methods
AU - Unger, Gerhard
AU - Holzmann, Markus
PY - 2020/9
Y1 - 2020/9
N2 - In this paper the discrete eigenvalues of elliptic second order differential operators in L
2 (R
n), n ∈ N, with singular δ-and δ
′-interactions supported on hypersurfaces are stud-ied. We show the self-adjointness of these operators and derive equivalent formulations for the eigenvalue problems involving boundary integral operators. These formulations are suitable for the numerical computations of the discrete eigenvalues and the corresponding eigenfunctions by boundary element methods. We provide convergence results and show numerical examples.
AB - In this paper the discrete eigenvalues of elliptic second order differential operators in L
2 (R
n), n ∈ N, with singular δ-and δ
′-interactions supported on hypersurfaces are stud-ied. We show the self-adjointness of these operators and derive equivalent formulations for the eigenvalue problems involving boundary integral operators. These formulations are suitable for the numerical computations of the discrete eigenvalues and the corresponding eigenfunctions by boundary element methods. We provide convergence results and show numerical examples.
KW - Boundary element method
KW - Discrete eigenvalues
KW - Elliptic differential operators
KW - Integral operators
KW - δ and δ -interaction
UR - http://www.scopus.com/inward/record.url?scp=85096184377&partnerID=8YFLogxK
U2 - 10.7153/oam-2020-14-39
DO - 10.7153/oam-2020-14-39
M3 - Article
SN - 1846-3886
VL - 14
SP - 555
EP - 599
JO - Operators and Matrices
JF - Operators and Matrices
IS - 3
M1 - OaM-14-39
ER -