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A singular perturbation problem for linear operators with an application to electrostatic and magnetostatic boundary and transmission problems
Author(s) -
Engl H. W.,
Kress R.,
Meister E.
Publication year - 1981
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670030118
Subject(s) - mathematics , mathematical analysis , boundary value problem , integral equation , banach space , operator (biology) , perturbation (astronomy) , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
The treatment of certain electro‐ and magnetostatic boundary and transmission problems by boundary integral equations leads to parameter‐dependent integral equations of the second kind. The integral operators involved have the property that the dimension of their nullspaces changes between two nonzero values (depending on the geometry of the problem) as the parameter tends to zero. We investigate the continuous dependence of solutions to these equations on the parameter. To this end, we treat the problem of continuous dependence of solutions to parameter‐dependent linear operator equations of the second kind in a Banach space in the framework of generalized inverses.