Nash-Moser iteration argument: Difference between revisions
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This iteration argument is mostly employed in very nonlinear situations, such as [[quasilinear]] equations, and tends to require a large amount of regularity. For [[semilinear]] equations the [[Duhamel iteration argument]] is usually more efficient and gives stronger results. | This iteration argument is mostly employed in very nonlinear situations, such as [[quasilinear]] equations, and tends to require a large amount of regularity. For [[semilinear]] equations the [[Duhamel iteration argument]] is usually more efficient and gives stronger results. | ||
[[Category: | [[Category:Methods]] | ||
Latest revision as of 00:13, 18 August 2006
The Nash-Moser iteration argument is an iteration scheme based upon Newton's method for finding roots of a nonlinear equation. In order to make the scheme converge, one needs to apply regularizing operators (such as Littlewood-Paley multipliers) between each iteration of Newton's method.
This iteration argument is mostly employed in very nonlinear situations, such as quasilinear equations, and tends to require a large amount of regularity. For semilinear equations the Duhamel iteration argument is usually more efficient and gives stronger results.
