We consider the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients. In order to avoid the problem of the formal coherence of the initial data, which leads to the notion of formally non-characteristic introduced by Andreotti-Nacinovich in the 80's, we allow formal solutions (in the sense of Whitney) of the given system on any closed subset as initial data. The problem is then to find classical smooth solutions of the system, whose restrictions in the sense of Whitney are the given initial data. This gives a unifying point of view encompassing several different problems, ranging from questions of smoothness of the solutions, to the classical Cauchy problem, to comparison of formal to actual solutions, to Hartog's type phenomena.

The overdetermined Cauchy problem

BOITI, Chiara;
1997

Abstract

We consider the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients. In order to avoid the problem of the formal coherence of the initial data, which leads to the notion of formally non-characteristic introduced by Andreotti-Nacinovich in the 80's, we allow formal solutions (in the sense of Whitney) of the given system on any closed subset as initial data. The problem is then to find classical smooth solutions of the system, whose restrictions in the sense of Whitney are the given initial data. This gives a unifying point of view encompassing several different problems, ranging from questions of smoothness of the solutions, to the classical Cauchy problem, to comparison of formal to actual solutions, to Hartog's type phenomena.
1997
Boiti, Chiara; M., Nacinovich
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/1198348
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 9
social impact