On the domain of the implicit function and applications
<p/> <p>The implicit function theorem asserts that there exists a ball of nonzero radius within which one can express a certain subset of variables, in a system of equations, as functions of the remaining variables. We derive a lower bound for the radius of this ball in the case of Lipsc...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2005-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2005/373250 |
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doaj-377258334d8f410a89bf11c0df2219552020-11-25T02:28:21ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2005-01-0120053373250On the domain of the implicit function and applicationsPapi Marco<p/> <p>The implicit function theorem asserts that there exists a ball of nonzero radius within which one can express a certain subset of variables, in a system of equations, as functions of the remaining variables. We derive a lower bound for the radius of this ball in the case of Lipschitz maps. Under a sign-preserving condition, we prove that an implicit function exists in the case of a set of inequalities. Also in this case, we state an estimate for the size of the domain. An application to the local Lipschitz behavior of solution maps is discussed.</p>http://www.journalofinequalitiesandapplications.com/content/2005/373250 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Papi Marco |
| spellingShingle |
Papi Marco On the domain of the implicit function and applications Journal of Inequalities and Applications |
| author_facet |
Papi Marco |
| author_sort |
Papi Marco |
| title |
On the domain of the implicit function and applications |
| title_short |
On the domain of the implicit function and applications |
| title_full |
On the domain of the implicit function and applications |
| title_fullStr |
On the domain of the implicit function and applications |
| title_full_unstemmed |
On the domain of the implicit function and applications |
| title_sort |
on the domain of the implicit function and applications |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1025-5834 1029-242X |
| publishDate |
2005-01-01 |
| description |
<p/> <p>The implicit function theorem asserts that there exists a ball of nonzero radius within which one can express a certain subset of variables, in a system of equations, as functions of the remaining variables. We derive a lower bound for the radius of this ball in the case of Lipschitz maps. Under a sign-preserving condition, we prove that an implicit function exists in the case of a set of inequalities. Also in this case, we state an estimate for the size of the domain. An application to the local Lipschitz behavior of solution maps is discussed.</p> |
| url |
http://www.journalofinequalitiesandapplications.com/content/2005/373250 |
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