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Degenerate cases of uniform approximation by solutions of systems with surjective symbols. (English) Zbl 0795.35003

Summary: We prove that each (vector-valued) function in Sobolev space on a compact set \(K\), which in the interior \(K^ 0\) of \(K\) satisfies a system of differential equations, can be approximated by solutions in a neighbourhood of \(K\) plus sums of potentials of measures supported on the boundary of \(K\). We discuss the particular case where, for all compact sets \(K\), one can dispense with potentials in such approximations.

MSC:

35A35 Theoretical approximation in context of PDEs
31B35 Connections of harmonic functions with differential equations in higher dimensions
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