PreprintarXiv licencearXiv
Revisiting Picard's proof of the Picard--Weber--Weck selection theorem
Abstract
Revisiting the rationale provided by Picard in the seminal paper [13], we provide an independent, self-contained proof of the Maxwell compactness property for weak Lipschitz domains in the Euclidean setting, detouring technical complications like the differential forms setting, Gaffney's inequality for smooth domains, Calderon's extension theorem or regularity theory for PDEs, or systems thereof, on smooth domains that are used in this context. As a by-product we provide an independent proof of the classical Gaffney estimate for cubes using only L2-completeness of the Fourier bases.
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BibTeX
@misc{lim2026revisiting,
title = {{Revisiting Picard's proof of the Picard--Weber--Weck selection theorem}},
author = {Yi-Sheng Lim and Timo Sprekeler and Marcus Waurick},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.31054},
eprint = {2608.31054},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.31054},
}
RIS
TY - UNPB
TI - Revisiting Picard's proof of the Picard--Weber--Weck selection theorem
AU - Yi-Sheng Lim
AU - Timo Sprekeler
AU - Marcus Waurick
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.31054
UR - https://arxiv.org/abs/2608.31054
AB - Revisiting the rationale provided by Picard in the seminal paper [13], we provide an independent, self-contained proof of the Maxwell compactness property for weak Lipschitz domains in the Euclidean setting, detouring technical complications like the differential forms setting, Gaffney's inequality for smooth domains, Calderon's extension theorem or regularity theory for PDEs, or systems thereof, on smooth domains that are used in this context. As a by-product we provide an independent proof of the classical Gaffney estimate for cubes using only L^2-completeness of the Fourier bases.
ER -