The inverse function theorem of Nash and Moser

Hamilton, Richard S.

doi:10.1090/S0273-0979-1982-15004-2

Author: Richard S. Hamilton
Journal: Bull. Amer. Math. Soc. 7 (1982), 65-222
MSC (1980): Primary 58C15; Secondary 58C20, 58D05, 58G30
DOI: https://doi.org/10.1090/S0273-0979-1982-15004-2
MathSciNet review: 656198
Full-text PDF Free Access

Andrew Acker, A free boundary optimization problem. II, SIAM J. Math. Anal. 11 (1980), no. 1, 201–209. MR 556510, DOI https://doi.org/10.1137/0511018
J. Thomas Beale, The existence of solitary water waves, Comm. Pure Appl. Math. 30 (1977), no. 4, 373–389. MR 445136, DOI https://doi.org/10.1002/cpa.3160300402
Nicole Desolneux-Moulis, Théorie du degré dans certains espaces de Fréchet, d’après R. S. Hamilton, Bull. Soc. Math. France Mém. 46 (1976), 173–180 (French). MR 440588, DOI https://doi.org/10.24033/msmf.193

4. R. S. Hamilton, Deformation of complex structures on manifolds with boundary.

Richard S. Hamilton, Deformation of complex structures on manifolds with boundary. I. The stable case, J. Differential Geometry 12 (1977), no. 1, 1–45. MR 477158
Richard S. Hamilton, Deformation of complex structures on manifolds with boundary. II. Families of noncoercive boundary value problems, J. Differential Geometry 14 (1979), no. 3, 409–473 (1980). MR 594711

4. R. S. Hamilton, III.Extension of complex structures, preprint, Cornell Univ.

5. R. S. Hamilton, Deformation theory of foliations, preprint, Cornell Univ.

Lars Hörmander, The boundary problems of physical geodesy, Arch. Rational Mech. Anal. 62 (1976), no. 1, 1–52. MR 602181, DOI https://doi.org/10.1007/BF00251855

7. Lars Hörmander, Implicit function theorems, lecture notes, Stanford Univ., 1977.

Howard Jacobowitz, Implicit function theorems and isometric embeddings, Ann. of Math. (2) 95 (1972), 191–225. MR 307127, DOI https://doi.org/10.2307/1970796

9. M. Kuranishi, Deformations of isolated singularities and $øverline \partial \sbb$, J. Differential Geometry.

O. A. Ladyženskaja and N. N. Ural′ceva, Équations aux dérivées partielles de type elliptique, Monographies Universitaires de Mathématiques, No. 31, Dunod, Paris, 1968 (French). Traduit par G. Roos. MR 0239273

11. Martin Lo, Isometric embeddings and deformations of surfaces with boundary in R3, thesis, Cornell Univ., 1981.

12. S. Lojasiewics, Jr. and E. Zehnder, An inverse function theorem in Fréchet spaces, preprint.

Jürgen Moser, A rapidly convergent iteration method and non-linear differential equations. II, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 20 (1966), 499–535. MR 206461
John Nash, The imbedding problem for Riemannian manifolds, Ann. of Math. (2) 63 (1956), 20–63. MR 75639, DOI https://doi.org/10.2307/1969989
Louis Nirenberg, The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math. 6 (1953), 337–394. MR 58265, DOI https://doi.org/10.1002/cpa.3160060303
L. Nirenberg, An abstract form of the nonlinear Cauchy-Kowalewski theorem, J. Differential Geometry 6 (1972), 561–576. MR 322321

17. P. H. Rabinowitz, Periodic solutions of non-linear hyperbolic partial differential equations. I, Comm. Pure Appl. Math. 20 (1967), 145-205; II, 22 (1968), 15-39.

David G. Schaeffer, The capacitor problem, Indiana Univ. Math. J. 24 (1974/75), no. 12, 1143–1167. MR 393798, DOI https://doi.org/10.1512/iumj.1975.24.24095
David G. Schaeffer, A stability theorem for the obstacle problem, Advances in Math. 17 (1975), no. 1, 34–47. MR 380093, DOI https://doi.org/10.1016/0001-8708%2875%2990085-7
Francis Sergeraert, Une généralisation du théorème des fonctions implicites de Nash, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A861–A863 (French). MR 259699
Francis Sergeraert, Un théorème de fonctions implicites sur certains espaces de Fréchet et quelques applications, Ann. Sci. École Norm. Sup. (4) 5 (1972), 599–660 (French). MR 418140
Francis Sergeraert, Une extension d’un théorème de fonctions implicites de Hamilton, Bull. Soc. Math. France Mém. 46 (1976), 163–171 (French). MR 494210

23. M. Spivak, A comprehensive introduction to differential geometry, vol. 5, Publish or Perish, Berkeley, Calif., 1979.

E. Zehnder, Generalized implicit function theorems with applications to some small divisor problems. I, Comm. Pure Appl. Math. 28 (1975), 91–140. MR 380867, DOI https://doi.org/10.1002/cpa.3160280104
K. Jittorntrum, An implicit function theorem, J. Optim. Theory Appl. 25 (1978), no. 4, 575–577. MR 511620, DOI https://doi.org/10.1007/BF00933522