36 citations · 234 across the 37 of their papers we have counts for
10 papers · 1 filter
Persistence of solutions to the Derivative Nonlinear Schrödinger equation in weighted Sobolev spaces
Alejandro J. Castro, Khumoyun Jabbarkhanov, Azamat Kassimbekov
In this paper we show the persistence property for solutions of the derivative nonlinear Schrödinger equation with initial data in weighted Sobolev spaces $H^{2}(\mathbb{R})\cap L^…
A note on the quartic generalized Korteweg-de Vries equation in weighted Sobolev spaces
Alejandro J. Castro, Amin Esfahani, Lyailya Zhapsarbayeva
In this paper we establish the persistence property for solutions of the quartic generalized Korteweg-de Vries equation with initial data in weighted Sobolev spaces $H^{s}(\mathbb{…
The Nonlinear Schrödinger-Airy equation in weighted Sobolev spaces
Alejandro J. Castro, Khumoyun Jabbarkhanov, Lyailya Zhapsarbayeva
We study the persistence property of the solution for the nonlinear Schrödinger-Airy equation with initial data in the weighted Sobolev space $H^{1/4}(\mathbb{R})\cap L^2(|x|^{2m}d…
Regularity of Fourier integral operators with amplitudes in general Hörmander classes
Alejandro J. Castro, Anders Israelsson, Wolfgang Staubach
We prove the global -boundedness of Fourier integral operators that model the parametrices for hyperbolic partial differential equations, with amplitudes in classical Hörmande…
Regularity properties of Schrödinger integral operators and general oscillatory integrals
Alejandro J. Castro, Anders Israelsson, Wolfgang Staubach +1
We introduce the notion of Schrödinger integral operators and prove sharp local and global regularity results for these (including propagators for the quantum mechanical harmonic o…
Global well-posedness for the nonlinear wave equation in analytic Gevrey spaces
Daniel Oliveira da Silva, Alejandro J. Castro
We obtain an asymptotic rate of decay for the radius of spatial analyticity of solutions to the nonlinear wave equation with initial data in the analytic Gevrey spaces.
Transference of local to global maximal estimates for dispersive partial differential equations
Alejandro J. Castro, Salvador Rodríguez-López, Wolfgang Staubach
In this paper we give an elementary proof for transference of local to global maximal estimates for dispersive PDEs. This is done by transferring local estimates for certain…
Homogenization of a parabolic Dirichlet problem by a method of Dahlberg
Alejandro J. Castro, Martin Strömqvist
Consider the linear parabolic operator in divergence form We employ a method of Dahlberg to show that the Dirich…
Boundedness of single layer potentials associated to divergence form parabolic equations with complex coefficients
Alejandro J. Castro, Kaj Nyström, Olow Sande
We consider parabolic operators of the form $$\partial_t+\mathcal{L},\ \mathcal{L}:=-\mbox{div}\, A(X,t)\nabla,$$ in $\mathbb R_+^{n+2}:=\{(X,t)=(x,x_{n+1},t)\in \mathbb R^{n}\time…
Solvability of the Dirichlet, Neumann and the regularity problems for parabolic equations with Hölder continuous coefficients
Alejandro J. Castro, Salvador Rodríguez-López, Wolfgang Staubach
We establish the -solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with Hölder-continuous diffusion coefficients, on…