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- W4300642511 abstract "We prove an abstract Nash-Moser implicit function theorem which, when applied to control and Cauchy problems for PDEs in Sobolev class, is sharp in terms of the loss of regularity of the solution of the problem with respect to the data. The proof is a combination of: (i) the iteration scheme by Hormander (ARMA 1976), based on telescoping series, and very close to the original one by Nash; (ii) a suitable way of splitting series in scales of Banach spaces, inspired by a simple, clever trick used in paradifferential calculus (for example, by M'etivier). As an example of application, we apply our theorem to a control and a Cauchy problem for quasi-linear perturbations of KdV equations, improving the regularity of a previous result. With respect to other approaches to control and Cauchy problems, the application of our theorem requires lighter assumptions to be verified." @default.
- W4300642511 created "2022-10-03" @default.
- W4300642511 creator A5024139933 @default.
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- W4300642511 date "2016-09-01" @default.
- W4300642511 modified "2023-09-23" @default.
- W4300642511 title "A Nash-Moser-Hormander implicit function theorem with applications to control and Cauchy problems for PDEs" @default.
- W4300642511 doi "https://doi.org/10.48550/arxiv.1609.00213" @default.
- W4300642511 hasPublicationYear "2016" @default.
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