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• W3086250286 abstract "For $partial Omega$ the boundary of a bounded and connected strongly Lipschitz domain in $mathbb{R}^{d}$ with $dgeq3$, we prove that any field $fin L^{2} (partial Omega ; mathbb{R}^{d})$ decomposes, in an unique way, as the sum of three silent vector fields---fields whose magnetic potential vanishes in one or both components of $mathbb{R}^dsetminuspartial Omega$. Moreover, this decomposition is orthogonal if and only if $partial Omega$ is a sphere. We also show that any $f$ in $L^{2} (partial Omega ; mathbb{R}^{d})$ is uniquely the sum of two silent fields and a Hardy function, in which case the sum is orthogonal regardless of $partial Omega$; we express the corresponding orthogonal projections in terms of layer potentials. When $partial Omega$ is a sphere, both decompositions coincide and match what has been called the Hardy-Hodge decomposition in the literature." @default.
• W3086250286 created "2020-09-21" @default.
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• W3086250286 date "2020-09-11" @default.
• W3086250286 modified "2023-10-18" @default.
• W3086250286 title "Decomposition of $L^{2}$-vector fields on Lipschitz surfaces: characterization via null-spaces of the scalar potential" @default.
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• W3086250286 doi "https://doi.org/10.48550/arxiv.2009.05337" @default.
• W3086250286 hasPublicationYear "2020" @default.
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