Revisiting Picard's proof of the Picard--Weber--Weck selection theorem

Yi-Sheng Lim; Timo Sprekeler; Marcus Waurick

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arXiv · 2608.31054

Revisiting Picard's proof of the Picard--Weber--Weck selection theorem

Yi-Sheng Lim·Timo Sprekeler·Marcus Waurick

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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 $L^2$-completeness of the Fourier bases.

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Yi-Sheng Lim, Timo Sprekeler, Marcus Waurick. 2026-08-31. Revisiting Picard's proof of the Picard--Weber--Weck selection theorem. https://arxiv.org/abs/2608.31054

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