DOI QR코드

DOI QR Code

A SIMPLE NASH-MOSER IMPLICIT FUNCTION THEOREM IN WEIGHTED BANACH SPACES

  • Published : 2003.05.01

Abstract

We prove a simplified version of the Nash-Moser implicit function theorem in weighted Banach spaces. We relax the conditions so that the linearized equation has an approximate inverse in different weighted Banach spaces in each recurrence step.

Keywords

Nash-Moser;Banach spaces;Sobolev spaces

References

  1. Lectures at Standford University, Summer Quarter Implicit function theorems L.Hormander
  2. Ann. of Math. v.63 The imbedding problem for Riemannian manifolds J.Nash https://doi.org/10.2307/1969989
  3. Trans. Amer. Math. Soc. v.181 Global regularity for ∂ on weakly pseudo-convex manifolds J.J.Kohn https://doi.org/10.2307/1996633
  4. Acta. Math. v.113 L² estimates and existence theorems for the ∂-operator L.Hormander https://doi.org/10.1007/BF02391775
  5. Proc. Nat. Acad. Sci. v.47 A new technique for the construction of solutions of nonlinear differential equations J.Moser https://doi.org/10.1073/pnas.47.11.1824
  6. Extension of CR structures on three dimensional compact pseudoconvex CR manifolds D.Catlin;S.Cho
  7. Bull. Amer. Math. Soc. v.7 The inverse function theorem of Nash and Moser R.Hamilton https://doi.org/10.1090/S0273-0979-1982-15004-2
  8. Annales Acad. Sci. Fenniae, Series A.I. Math. v.10 On the Nash-Moser implicit function theorem L.Hormander https://doi.org/10.5186/aasfm.1985.1028
  9. J. Geom. Anal. v.4 Sufficient conditions for the extension of CR structures D.Catlin https://doi.org/10.1007/BF02922141
  10. Enseign. Math. v.35 no.2 A simple Nash-Moser implicit function theorem S.X.Raymond
  11. Arch. Rat. Mech. Anal. v.62 The boundary problems of physical geodesy L.Hormander
  12. Pacific J. of Math. v.207 Embedding of pseudoconvex CR manifolds with Levi-forms one degenerate eigenvalue S.Cho https://doi.org/10.2140/pjm.2002.207.311