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Factor-Analysis of nonlinear mappings: p-regularity theory

Tret'yakov, Alexey and Marsden, Jerrold E. (2003) Factor-Analysis of nonlinear mappings: p-regularity theory. Communications on Pure and Applied Analysis, 2 (4). pp. 425-445. ISSN 1534-0392. doi:10.3934/cpaa.2003.2.425.

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The paper presents recent advances in p-regularity theory, which has been developing successfully for the last twenty years. The main result of this theory gives a detailed description of the structure of the zero set of an irregular nonlinear mapping. We illustrate the theory with an application to degenerate problems in different fields of mathematics, which substantiates the general applicability of the class of p-regular problems. Moreover, the connection between singular problems and nonlinear mappings is shown. Amongst the applications, the structure of p-factor-operators is used to construct numerical methods for solving degenerate nonlinear equations and optimization problems.

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Additional Information:© 2003, AMS. Received December 2002; revised June 2003. Communicated by Steve Shkoller. We heartily thank Olga Brezhneva for the great help she provided us in writing this paper.
Subject Keywords:p-regularity, Lyusternik theorem, singularity, nonlinear mapping, bifurcation, factor operator, optimality conditions, implicit function, numerical method, differential equations.
Issue or Number:4
Classification Code:2000 MSC: Primary: 58C15, 58K05, 35B32, 37G10, 49K27,46N10. Secondary: 49N60, 90C30, 65J15.
Record Number:CaltechAUTHORS:20100916-153938212
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19994
Deposited By: Ruth Sustaita
Deposited On:17 Sep 2010 21:31
Last Modified:08 Nov 2021 23:56

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