相关论文: Strichartz estimates for the Schr\"odinger equatio…
We study the $L^p-L^q$-type uniform resolvent estimates for 2D-Schr\"odinger operators in scaling-critical magnetic fields, involving the Aharonov-Bohm model as a main example. As an application, we prove localization estimates for the…
In this note we obtain some Strichartz estimates for the Schr\"odinger equation associated to the twisted Laplacian on $\mathbb{C}^{n}\cong \mathbb{R}^{2n}$. The initial data will be considered in suitable Sobolev spaces associated to the…
We prove existence results for a stationary Schr{\"o}dinger equation with periodic magnetic potential satisfying a local integrability condition on the whole space using a critical value function.
We consider the $1d$ cubic nonlinear Schr\"odinger equation with a large external potential $V$ with no bound states. We prove global regularity and quantitative bounds for small solutions under mild assumptions on $V$. In particular, we do…
We consider continuum one-dimensional Schr\"odinger operators with potentials that are given by a sum of a suitable background potential and an Anderson-type potential whose single-site distribution has a continuous and compactly supported…
We obtain the global well-posedness for Schr\"odinger equations of higher orders in weighted $L^2$ spaces. This is based on weighted $L^2$ Strichartz estimates for the corresponding propagator with higher-order dispersion. Our method is…
In this paper, we prove Strichartz estimates for many body Schr\"odinger equations in the periodic setting, specifically on tori $\mathbb{T}^d$, where $d\geq 3$. The results hold for both rational and irrational tori, and for small…
We consider the inverse problem of determining the time dependent magnetic field of the Schr\"odinger equation in a bounded open subset of $R^n$, with $n \geq 1$, from a finite number of Neumann data, when the boundary measurement is taken…
We establish Strichartz estimates, including estimates involving spatial derivatives, for radial wave equations with potentials in similarity variables. This is accomplished for all spatial dimensions $d\geq 3$ and almost all regularities…
We prove almost Strichartz estimates found after adding regularity in the spherical coordinates for Schr\"odinger-like equations. The estimates are sharp up to endpoints. The proof relies on estimates involving spherical averages. Sharpness…
In this paper we are concerned with the existence and multiplicity of solutions for the fractional Choquard-type Schr\"{o}dinger-Kirchhoff equations with electromagnetic fields and critical nonlinearity: \begin{eqnarray*} \begin{cases}…
We prove Strichartz-type estimates for Schroedinger's equation with time-dependent potentials. The time derivative of the potentials need not be integrable, so the total variation of the potentials may be infinite.
We prove weighted $L^2$ estimates for the Klein-Gordon equation perturbed with singular potentials such as the inverse-square potential. We then deduce the well-posedness of the Cauchy problem for this equation with small perturbations, and…
Under natural energy and decay assumptions, we derive a priori estimates for solutions of a Schrodinger-Newton type of equation with critical exponent. On one hand, such an equation generalizes the traditional Schrodinger-Newton and…
Much of the literature on point interactions in quantum mechanics has focused on the differential form of Schr\"odinger's equation. This paper, in contrast, investigates the integral form of Schr\"odinger's equation. While both forms are…
We establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the case of wave, Klein-Gordon and fractional Schr\"odinger equations. Our results generalize the classical (single-function) Strichartz…
We study the semi-classical trace formula at a critical energy level for a Schr\"odinger operator on $\mathbb{R}^{n}$. We assume here that the potential has a totally degenerate critical point associated to a local minimum. The main result,…
We prove a weighted Carleman estimate for a class of one-dimensional, self-adjoint Schr\"odinger operators $P(h)$ with low regularity electric and magnetic potentials, where $h > 0$ is a semiclassical parameter. The long range part of…
We study local in time Strichartz estimates for the Schroedinger equation associated to long range perturbations of the flat Laplacian on the euclidean space. We prove that in such a geometric situation, outside of a large ball centered at…
We prove global Strichartz estimates without loss for the wave equation outside two strictly convex obstacles, following the roadmap introduced in [Lafontaine, 2017] for the Schr\"odinger equation. Moreover, we show a first step toward the…