Gauthier, P. M.; Tarkhanov, N. N. Degenerate cases of uniform approximation by solutions of systems with surjective symbols. (English) Zbl 0795.35003 Can. J. Math. 45, No. 4, 740-757 (1993). 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. Cited in 2 Documents MSC: 35A35 Theoretical approximation in context of PDEs 31B35 Connections of harmonic functions with differential equations in higher dimensions Keywords:Sobolev space; measures supported on the boundary PDFBibTeX XMLCite \textit{P. M. Gauthier} and \textit{N. N. Tarkhanov}, Can. J. Math. 45, No. 4, 740--757 (1993; Zbl 0795.35003) Full Text: DOI