My updated website is now at BCAM

 
 
 
 
 
 
 
 
 
 

 

The Dynamics of Vortex Filaments with Corners [pdf]
Subjects: Analysis of PDEs 
 
arXiv:1304.0996 [pdf, other]
The initial value problem for the binormal flow with rough data
Comments: 33 pages, 3 figures
Subjects: Analysis of PDEs (math.AP)
Vortex Filament Equation for a Regular Polygon [pdf]
Subjects: Analysis of PDEs (math.AP)
arXiv:1303.2519 [pdf, ps, other]
Shell interactions for Dirac operators
Subjects: Analysis of PDEs (math.AP)
arXiv:1211.5476 [pdf, ps, other]
Self-adjoint extensions of Dirac operators with Coulomb type singularity
Comments: Submitted
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)
arXiv:1211.1030 [pdf, ps, other]
The forward problem for the electromagnetic Helmholtz equation with critical singularities
Subjects: Analysis of PDEs (math.AP)
arXiv:1202.1106 [pdf, ps, other]
Stability of the selfsimilar dynamics of a vortex filament
Comments: 30 pages
Subjects: Analysis of PDEs (math.AP)
arXiv:1201.5587 [pdf, ps, other]
A Theorem of Paley-Wiener Type for Schrödinger Evolutions
Comments: 19 pages
Subjects: Analysis of PDEs (math.AP)
arXiv:1112.3505 [pdf, ps, other]
Lower Bounds for Non-Trivial Traveling Wave Solutions of Equations of KdV Type
Subjects: Analysis of PDEs (math.AP)
arXiv:1111.0277 [pdf, ps, other]
Scattering for solutions of NLS in the exterior of a 2d star--shaped obstacle
Comments: Final version to appear in Math. Res. Lett
Subjects: Analysis of PDEs (math.AP)
arXiv:1110.4873 [pdf, ps, other]
Uniqueness Properties of Solutions to Schrödinger Equations
Subjects: Analysis of PDEs (math.AP)
arXiv:1109.6028 [pdf, ps, other]
Discrete conservation laws and the convergence of long time simulations of the mKdV equation
Comments: 22 pages, 7 figures
Subjects: Numerical Analysis (math.NA); Exactly Solvable and Integrable Systems (nlin.SI)
arXiv:1105.3230 [pdf, ps, other]
Carleman estimates and necessary conditions for the existence of waveguides
Comments: 12 pages
Subjects: Analysis of PDEs (math.AP)
arXiv:1103.5403 [pdf, ps, other]
On the stability of self-similar solutions of 1D cubic Schrodinger equations
Comments: 38 pages, 8 figures
Subjects: Analysis of PDEs (math.AP)
 
arXiv:1103.4925 [pdf, ps, other]
Selfsimilar solutions of the binormal flow and their stability
Comments: 36 pages, survey to appear in Panoramas et Synth`eses
Subjects: Analysis of PDEs (math.AP)
arXiv:1103.4751 [pdf, ps, other]
Existence of maximizers for Sobolev-Strichartz inequalities
Comments: 10 pages
Subjects: Analysis of PDEs (math.AP)
arXiv:1012.5290 [pdf, ps, other]
The Gardner equation and the L^2-stability of the N-soliton solution of the Korteweg-de Vries equation
Comments: 19 pages, final version incorporating referee's comments. To appear in TAMS
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)
arXiv:1010.1906 [pdf, ps, other]
Unique Continuation for Schrödinger Evolutions, with applications to profiles of concentration and traveling waves
Comments: 23 pages
Subjects: Analysis of PDEs (math.AP)
arXiv:1007.2063 [pdf, ps, other]
On the existence of maximizers for a family of Restriction Theorems
Comments: 6 pages
Subjects: Analysis of PDEs (math.AP)
arXiv:1005.1543 [pdf, ps, other]
The Hardy Uncertainty Principle Revisited
Subjects: Analysis of PDEs (math.AP)
arXiv:0909.4111 [pdf, ps, other]
Stability in $L^1$ of circular vortex patches
Subjects: Analysis of PDEs (math.AP)
arXiv:0909.3287 [pdf, ps, other]
Uncertainty Principle of Morgan type and Schrödinger Evolutions
Subjects: Analysis of PDEs (math.AP)
arXiv:0906.0884 [pdf, ps, other]
The sharp Hardy Uncertainty Principle for Schödinger evolutions
Subjects: Analysis of PDEs (math.AP); Classical Analysis and ODEs (math.CA)
 arXiv:0905.0062 [pdf, ps, other]
Scattering for 1D cubic NLS and singular vortex dynamics
Comments: 42 pages, revised version, to appear in J. Eur. Math. Soc
Subjects: Analysis of PDEs (math.AP)
arXiv:0901.4024 [pdf, ps, other]
Endpoint Strichartz estimates for the magnetic Schrodinger equation
Comments: 11 pages
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)
arXiv:0812.1011 [pdf, other]
A numerical study of the self-similar solutions of the Schroedinger Map
Subjects: Numerical Analysis (math.NA); Analysis of PDEs (math.AP)
arXiv:0806.0778 [pdf, ps, other]
Magnetic virial identities, weak dispersion and Strichartz inequalities
Comments: 23 pages, misprint in the title of the previous version
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)
arXiv:0805.0205 [pdf, ps, other]
On the equipartition of energy for critical NLW
Comments: to appear on Journal of Functional Analysis
Subjects: Analysis of PDEs (math.AP)
arXiv:0804.2313 [pdf, ps, other]
Scaling-sharp dispersive estimates for the Korteweg-de Vries group
Raphaël Côte (CMLS-EcolePolytechnique), Luis Vega
Comments: 5 pages
Subjects: Analysis of PDEs (math.AP)
arXiv:0802.2161 [pdf, ps, other]
Weak Dispersive estimates for Schrödinger equations with long range potentials
Comments: 29 pages
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)
arXiv:0802.1996 [pdf, ps, other]
On the stability of a singular vortex dynamics
Valeria Banica (DP), Luis Vega (BILBAO)
Comments: 35 pages, revised version, to appear in Comm. Math. Phys
Subjects: Analysis of PDEs (math.AP)
arXiv:0802.1608 [pdf, ps, other]
Hardy's Uncertainty Principle, Convexity and Schrödinger Evolutions
Subjects: Analysis of PDEs (math.AP)
arXiv:0712.4076 [pdf, ps, other]
Bilinear virial identities and applications
Comments: 30 pages, final version to appear in the Annales Scientifiques de l'ENS
Subjects: Analysis of PDEs (math.AP)
arXiv:0712.3648 [pdf, ps, other]
Asymptotic Lower Bounds for a class of Schroedinger Equations
Comments: 24 pages. to appear on Comm. Math. Phys
Subjects: Analysis of PDEs (math.AP)
arXiv:0710.2144 [pdf, ps, other]
Convexity properties of solutions to the free Schrödinger equation with Gaussian decay
Comments: 19 pages
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)
arXiv:0706.0819 [pdf, ps, other]
On the Dirac delta as initial condition for nonlinear Schrödinger equations
Valeria Banica (DP), Luis Vega (BILBAO)
Comments: 17 pages, to appear in in AnIHP Ann Non Lin
Subjects: Analysis of PDEs (math.AP)
arXiv:math/0703037 [pdf, ps, other]
Local well-posedness for the modified KdV equation in almost critical ^H^r_s-spaces
Comments: 12 pages
Subjects: Analysis of PDEs (math.AP)
arXiv:math/0612481 [pdf, ps, other]
Schrödinger Maps and their associated Frame Systems
Comments: 19 pages, submitted
Subjects: Analysis of PDEs (math.AP); Differential Geometry (math.DG)
arXiv:math/0609109 [pdf, ps, other]
On the Local Smoothing for a class of conformally invariant Schroedinger equations
Subjects: Analysis of PDEs (math.AP)
arXiv:math/0609108 [pdf, ps, other]
On the Local Smoothing for the Schroedinger Equation
Subjects: Analysis of PDEs (math.AP)
arXiv:math/0607801 [pdf, ps, other]
Energy concentration and Sommerfeld condition for Helmholtz equation with variable index at infinity
Benoit Perthame (DMA), Luis Vega (DMA)
Subjects: Analysis of PDEs (math.AP)
arXiv:math/0602257 [pdf, ps, other]
Counterexamples of Strichartz Inequalities for Schrodinger Equations with Repulsive Potentials
Comments: 13 pages. Corrected typo in arXiv abstract. No changes to paper itself
Journal-ref: Intl. Math. Res. Not. 2006 (2006), Article ID 13927, 16pp.
Subjects: Analysis of PDEs (math.AP)
arXiv:math/0601621 [pdf, ps, other]
On uniqueness properties of solutions of the k-generalized KdV equations
Subjects: Analysis of PDEs (math.AP)
arXiv:math/0509436 [pdf, ps, other]
Decay at infinity of caloric functions within characteristic hyperplanes
Subjects: Analysis of PDEs (math.AP)
arXiv:math/0509199 [pdf, ps, other]
On unique continuation of solutions of Schrödinger equations
Subjects: Analysis of PDEs (math.AP)
arXiv:math/0503206 [pdf, ps, other]
The General Quasilinear Ultrahyperbolic Schrödinger Equation
Comments: 29 pages
Subjects: Analysis of PDEs (math.AP)
arXiv:math/0503205 [pdf, ps, other]
Variable coefficient Schrödinger flows for ultrahyperbolic operators
Subjects: Analysis of PDEs (math.AP)
arXiv:math/0404291 [pdf, ps, other]
Self-binormal solutions of the Localized Induction Approximation: Singularity formation
Susana Gutierrez (University of Edinburgh), Luis Vega (Basque Country University)
Comments: 60 pages, 8 figures
Subjects: Analysis of PDEs (math.AP)
arXiv:math-ph/0309065 [pdf, ps, other]
An analytical proof of Hardy-like inequalities related to the Dirac operator
Comments: LaTex, 22 pages
Subjects: Mathematical Physics (math-ph)
arXiv:math/0009065 [pdf, ps, other]
On the support of solutions to the g-KdV equation
Subjects: Analysis of PDEs (math.AP)
arXiv:math/9807163 [pdf, ps, other]
A bilinear approach to the restriction and Kakeya conjectures
Comments: 33 pages, 3 figures, LaTeX, to appear JAMS
Subjects: Classical Analysis and ODEs (math.CA)