A local inversion principle of the Nash-Moser type

被引：1
作者：
Castro, A [1 ]
Neuberger, JW
机构：
[1] Univ Texas, Div Math & Stat, San Antonio, TX 78249 USA
[2] Univ N Texas, Dept Math, Denton, TX 76203 USA
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2001年 / 33卷 / 04期
关键词：
Nash-Moser methods; inverse function theorem; continuous steepest descent;
D O I：
10.1137/S0036141099357690
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove an inverse function theorem of the Nash-Moser type. The main difference between our method and that of [J. Moser, Proc. Nat. Acad. Sci. USA, 47 (1961), pp. 1824-1831] is that we use continuous steepest descent while Moser uses a combination of Newton-type iterations and approximate inverses. We bypass the loss of derivatives problem by working on finite-dimensional subspaces of infinitely differentiable functions.
引用
收藏
页码：989 / 993
页数：5
相关论文
共 12 条
[1]  
CASTRO A, 1999, CONT MATH, V221, P127
[2]   THE INVERSE FUNCTION THEOREM OF NASH AND MOSER [J].
HAMILTON, RS .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 7 (01) :65-222
[3]  
HORMANDER L, 1985, ANN ACAD SCI FENN-M, V10, P255
[4]  
KORMAN P, 1989, COMMUN PART DIFF EQ, V14, P519
[5]   NEW TECHNIQUE FOR CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS [J].
MOSER, J .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1961, 47 (11) :1824-&
[6]  
Moser J., 1966, Annali della Scuola Normale Superiore di Pisa-Scienze Fisiche e Matematiche, V3, P265
[7]  
Neuberger J. W., 1997, Lecture Notes in Math., V1670
[8]  
NEUBERGER JW, 1985, J MATH SOC JPN, V37, P187
[9]   CONSTRUCTIVE VARIATIONAL-METHODS FOR DIFFERENTIAL-EQUATIONS [J].
NEUBERGER, JW .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1989, 13 (04) :413-428
[10]   An inverse function theorem for Frechet spaces satisfying a smoothing property and (DN) [J].
Poppenberg, M .
MATHEMATISCHE NACHRICHTEN, 1999, 206 :123-145
12