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Vector potentials in the half-space of \(\mathbb{R}^3\). (English. Abridged French version) Zbl 0981.35013
Summary: We prove a class of results concerning the vector potentials of divergence-free fields in a half-space of \(\mathbb{R}^3\). A family of weighted spaces is used as a framework for describing the growth or the decay of functions at infinity.

MSC:
35F05 Linear first-order PDEs
35N10 Overdetermined systems of PDEs with variable coefficients
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