## 1,129 Citations

On the Cauchy problem of dispersive Burgers type equations

- Mathematics
- 2021

We study the paralinearised weakly dispersive Burgers type equation: ∂tu+ ∂x[Tuu]− T ∂xu 2 u+ ∂x |D| α−1 u = 0, α ∈]1, 2[, which contains the main non linear ”worst interaction” terms, i.e low-high…

A Category of Banach Space Functors.

- Mathematics
- 2020

We consider the problem of normal forms from an abstract perspective. We introduce a functorial viewpoint on functional analysis, develop functional calculus and prove a general versal deformation…

Symplectic Manifolds and Isomonodromic Deformations.

- Mathematics
- 2020

We study moduli spaces of meromorphic connections (with arbitrary order poles) over Riemann surfaces together with the corresponding spaces of monodromy data (involving Stokes matrices). Natural…

Condições de transversalidades na mecânica

- Physics
- 2019

Neste trabalho nos mostramos a deducao da equacao de Euler-Lagrange e das condicoes de transversalidade em um contexto geometrico. Para isto, consideramos um funcional F, medindo algum aspecto fisico…

Exact controllability for quasilinear perturbations of KdV

- Mathematics
- 2017

We prove that the KdV equation on the circle remains exactly controllable in arbitrary time with localized control, for sufficiently small data, also in presence of quasi-linear perturbations, namely…

On geodesic completeness for Riemannian metrics on smooth probability densities

- Mathematics
- 2017

The geometric approach to optimal transport and information theory has triggered the interpretation of probability densities as an infinite-dimensional Riemannian manifold. The most studied…

A Nash-Moser-H\"ormander implicit function theorem with applications to control and Cauchy problems for PDEs

- Mathematics
- 2016

On a certain type of nonlinear hyperbolic equations derived from astrophysical problems

- Mathematics, Physics
- 2016

Investigations of spherically symmetric motions of self-gravitating gaseous stars governed by the non-relativistic Newtonian gravitation theory or by the general relativistic theory lead us to a…

Rigidity of actions on presymplectic manifolds

- Mathematics
- 2016

We prove the rigidity of presymplectic actions of a compact semisimple Lie algebra on a presymplectic manifold of constant rank in the local and global case. The proof uses an abstract normal form…

On spherically symmetric solutions of the Einstein-Euler-de Sitter equations

- Mathematics, Physics
- 2015

We construct spherically symmetric solutions to the Einstein-Euler equations, which contains a positive cosmological constant, say, the EinsteinEuler-de Sitter equations. We assume a realistic…

## References

SHOWING 1-10 OF 22 REFERENCES

A rapidly convergent iteration method and non-linear partial differential equations - I

- Mathematics
- 1966

L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions…

Generalized implicit function theorems with applications to some small divisor problems, I

- Mathematics
- 1976

Isometric embeddings and deformations of surfaces with boundary in R3

- thesis, Cornell Univ.,
- 1981

Deformation of complex structures on manifolds with boundary. II. Families of noncoercive boundary value problems

- Mathematics
- 1979

A skate sharpener having a cylindrical sharpening member held between two symmetrical members forming a holder. A radical slot is provided in the holder for receiving a skate blade to be sharpened by…

A Free Boundary Optimization Problem

- Mathematics
- 1978

Given a convex set $Q \subset R^2 $ (bounded by a simple closed curve) and a constant $A > 0$, we determine the doubly-connected region $\Omega $ encircling (but not intersecting) Q, with area $|…

An implicit function theorem

- Mathematics
- 1978

Suppose thatF:D⊂Rn×Rm→Rn, withF(x0,y0)=0. The classical implicit function theorem requires thatF is differentiable with respect tox and moreover that ∂1F(x0,y0) is nonsingular. We strengthen this…

The boundary problems of physical geodesy

- Geology, Physics
- 1976

The purpose of this paper is to discuss the determination of the figure of the earth and its gravity field from astrogeodetic and gravimetric data. (By gravity we mean the resultant of the attractive…