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Degenerate Cases of Uniform Approximation by Solutions of Systems with Surjective Symbols

Published online by Cambridge University Press:  20 November 2018

P. M. Gauthier
Affiliation:
Département de mathématiques et de satistique et Centre de recherches mathématiques Université de Montréal, CP 6128-A Montreal, Québec H3C 3J7 e-mail: [email protected]
N. N. Tarkhanov
Affiliation:
Institute of Physics and Krasnoyarsk University Rossiya
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Abstract

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We prove that each (vector-valued) function in Sobolev space on a compact set K, which in the interior K0 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

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1993

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