| | |
| | |
Stat |
Members: 3667 Articles: 2'599'751 Articles rated: 2609
07 February 2025 |
|
| | | |
|
Article overview
| |
|
A Nash-Moser-H"ormander implicit function theorem with applications to control and Cauchy problems for PDEs | Pietro Baldi
; Emanuele Haus
; | Date: |
1 Sep 2016 | 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 H"ormander (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. | Source: | arXiv, 1609.0213 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
|
| |
|
|
|