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On continuation of quasi-analytic solutions of partial differential equations to compact convex sets

Published online by Cambridge University Press:  09 April 2009

Wojciech Abramczuk
Affiliation:
Department of Mathematics, University of Stockholm, Stockholm, Sweden
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Abstract

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In the early 70s A. Kaneko studied the problem of continuation of regular solutions of systems of linear partial differential equations with constant coefficients to compact convex sets. We show here that the conditions be obtained for real analytic solutions also hold in the quasi-analytic case. In particular we show that every quasi-analytic solution of the system p(D)u = 0 defined outside a compact convex subset K or Rn can be continued as a quasi-analytic solution to K if and only if the system is determined and the -module Ext1(Coker p′, ) has no elliptic component; here is the ring of polynomials in n variables, p is a matrix with elements from and p′ is the transposed matrix. In the scalar case, i.e. when p is a single polynomial, these conditions mean that p has no elliptic factor.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1985

References

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