@article{7d112cb8b72240ba9c7a926f1e930d15,
title = "Closed-Form Inverses of the Weakly Singular and Hypersingular Operators on Disks",
abstract = "We establish new explicit expressions and variational forms of boundary integral operators that provide the exact inverses of the weakly singular and hypersingular operators for - Δ on flat disks. We derive closed-form formulas for their singular kernels. We also show that the inverse of the weakly singular operator can be obtained by composing surface curl operators and the inverse of the hypersingular operator.",
keywords = "Boundary integral operators, Exact inverses, Projected spherical harmonics, Screens",
author = "R. Hiptmair and C. Jerez-Hanckes and C. Urz{\'u}a-Torres",
note = "Funding Information: The work of the second author was partially funded by Chile CORFO Engineering 2030 program through Grant OPEN-UC 201603, Conicyt Anillo ACT1417 and Fondecyt Regular 1171491. The work of the third author was supported by ETHIRA Grant ETH-04 13-2. Publisher Copyright: {\textcopyright} 2018, Springer International Publishing AG, part of Springer Nature.",
year = "2018",
month = feb,
day = "1",
doi = "10.1007/s00020-018-2425-y",
language = "English",
volume = "90",
journal = "Integral Equations and Operator Theory",
issn = "0378-620X",
number = "1",
}