On the existence of real analytic solutions of partial differential equations with constant coefficients

1973 ◽  
Vol 21 (3) ◽  
pp. 151-182 ◽  
Author(s):  
Lars H�rmander
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytic Solutions ◽  
Partial Differential ◽  
Constant Coefficients ◽  
Real Analytic ◽  
Real Analytic Solutions

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

1985 ◽  
Vol 39 (3) ◽  
pp. 306-316 ◽  
Author(s):  
Wojciech Abramczuk
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Convex Sets ◽  
Analytic Solution ◽  
Compact Convex ◽  
Analytic Solutions ◽  
Scalar Case ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Constant Coefficients

AbstractIn 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.

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