Sufficiency of condition (Ψ) for local solvability in two dimensions

@article{Lerner1988SufficiencyOC,
  title={Sufficiency of condition ($\Psi$) for local solvability in two dimensions},
  author={Nicolas Lerner},
  journal={Annals of Mathematics},
  year={1988},
  volume={128},
  pages={243-258}
}
  • N. Lerner
  • Published 1 September 1988
  • Mathematics
  • Annals of Mathematics
On etablit l'existence de solutions locales de l'equation Pu=f ou P est un operateur pseudodifferentiel classique a 2 dimensions de type principal, d'ordre m qui satisfait la condition (Ψ): la partie imaginaire p 2 du symbole principal de P ne change pas de signe de − a + le long d'une bicaracteristique orientee de la partie reelle p 1 du symbole principal 
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References

SHOWING 1-10 OF 11 REFERENCES
Théorie des distributions à valeurs vectorielles. I
© Annales de l’institut Fourier, 1957, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions
On Local Solvability of Linear Partial Differential Equations
The title indicates more or less what the talk is going to be about. I t is going to be about the problem which is probably the most primitive in partial differential equations theory, namely to know
The analysis of linear partial differential operators
the analysis of linear partial differential operators i distribution theory and fourier rep are a good way to achieve details about operating certainproducts. Many products that you buy can be
The cajionical transformations of pseudo-differential operators^ Uspehi Mat
  • Nauk
  • 1969
Theorie des distributions a vaJeurs vectorieJJes
  • I. Ann. Inst. Fourier
  • 1957
LocaJ solvability in two dimensions: necessary conditions for the principle-type case. University of Kansas. Mimeographed manuscript
    11)) we obtain the lemma for Re^^a^ + Ci)) and we can neglect the term C\ by using the large constant 6^1 in (2.20). The proof is complete
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