An abstract Nash-Moser theorem with parameters and applications to PDEs

By Massimiliano Berti, P. Bolle, Michela Procesi. 2010

84 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/30de54db235a41cf04740b8cacb0d51a1d8a97e8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Massimiliano Berti
2. Michela Procesi
3. P. Bolle
4. Luca Biasco
5. Pierre Baldi
6. Livia Corsi
7. C. Procesi
8. Berti M

In Numerical Analysis

1. Massimiliano Berti
2. P. Bolle
3. Michela Procesi
4. Pierre Baldi
5. Livia Corsi
6. E. Haus
7. Riccardo Montalto
8. Luca Biasco

In Statistical and Nonlinear Physics

1. Massimiliano Berti
2. Michela Procesi
3. Riccardo Montalto
4. P. Bolle
5. Pierre Baldi
6. E. Haus
7. Livia Corsi
8. Luca Biasco

Citations in the corpus

• Time quasi-periodic gravity water waves in finite depth (2017, background): “The main advantage with respect to the Nash-Moser implicit function theorems as presented in [62, 17] is the optimal regularity of the solution u in terms of the datum g (see (B.”
• Branching of Cantor Manifolds of Elliptic Tori and Applications to PDEs (2011, background): “Craig-Wayne [14], Bourgain [8]-[10], Berti-Bolle [5] and with Procesi [6].”
• Nonlinear wave and Schrödinger equations on compact Lie groups and homogeneous spaces (2011, methodology): “These could also be used to prove existence of small amplitude periodic solutions (however this result has been recently achieved in [5] with simpler methods).”
• Quasi-periodic solutions with Sobolev regularity of NLS on T^d with a multiplicative potential (2010, methodology): “9) is given for example in Appendix of [4], see also [31].”
• KAM for quasi-linear and fully nonlinear forced perturbations of Airy equation (2014, unknown): “It is especially convenient for PDEs in higher space dimension, because of the high multiplicity of the eigenvalues: see also the recent results by Wang [41], Berti-Bolle [7], [8] (and [9], [22] for periodic solutions).”
• Quasi-periodic solutions with Sobolev regularity of NLS on $\mathbb {T}^d$ with a multiplicative potential (2013, methodology): “9) is given for example in Appendix of [4], see also [31].”
• An Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds (2013, background): “1 in [6]): for all s1 < s2, t ∈ [0, 1], ‖u‖ts1+(1−t)s2 ≤ K(s1, s2)‖u‖ts1‖u‖1−t s2 .”