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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  and
N. N. Tarkhanov
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: gauthier@ere.umontrealca
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

Keywords

35A3531B35elliptic systemssurjective symbolsuniform approximation
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 4 , 01 August 1993 , pp. 740 - 757
Copyright
Copyright © Canadian Mathematical Society 1993

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