Related papers: Sharp Gaussian upper bounds for Schr\"odinger semi…
We prove sharp Strichartz estimates for the semi-classical Schrodinger equation on a compact manifold with smooth, strictly geodesically concave boundary. We deduce sharp (classical) Strichartz estimates for the Schrodinger equation outside…
We prove a Gaussian upper bound for the fundamental solutions of a class of ultra-parabolic equations in divergence form. The bound is independent on the smoothness of the coefficients and generalizes some classical results by Nash, Aronson…
We review some results concerning the semi-classical limit for the nonlinear Schrodinger equation, with or without an external potential. We consider initial data which are either of the WKB type, or very concentrated as the semi-classical…
We improve the result by Feola and Iandoli [J. de Math. Pures et App., 157:243-281, 2022], showing that quasilinear Hamiltonian Schr\"odinger type equations are well posed on $H^s(\mathbb{T}^d)$ if $s>d/2+3$. We exploit the sharp…
We present the maximally supersymmetric three-dimensional gauged supergravities. Owing to the special properties of three dimensions -- especially the on-shell duality between vector and scalar fields, and the purely topological character…
We give an elementary proof of a weighted resolvent estimate for semiclassical Schr\"odinger operators in dimension $n \ge 1$. We require the potential belong to $L^\infty(\mathbb{R}^n)$ and have compact support, but do not require that it…
We introduce a new, more general type of nonlinear gauge transformation in nonrelativistic quantum mechanics that involves derivatives of the wave function and belongs to the class of B\"acklund transformations. These transformations…
The present paper is devoted to the semiclassical analysis of linear Schr\"odinger equations from a Gabor frame perspective. We consider (time-dependent) smooth Hamiltonians with at most quadratic growth. Then we construct higher order…
The torsion index of split simple groups has been extensively studied, notably by Totaro, who calculated the torsion indexes of the spin groups and $E_{8}$ in [5] and [6], respectively. The aim of this paper is to provide upper bounds for…
This paper develops a novel operator theoretic framework to study the contraction properties of Markov semigroups with respect to a general class of Kantorovich semi-distances, which notably includes Wasserstein distances. The rather simple…
We prove upper and lower bounds for the number of lines in general position that are rich in a Cartesian product point set. This disproves a conjecture of Solymosi and improves work of Elekes, Borenstein and Croot, and Amirkhanyan, Bush,…
We are interested in a WKB analysis of the Logarithmic Non-Linear Schr\"odinger Equation with "Riemann-like" variables in an analytic framework in semiclassical regime. We show that the Cauchy problem is locally well posed uniformly in the…
We prove global well-posedness for the cubic, defocusing, nonlinear Schr{\"o}dinger equation on $\mathbf{R}^{2}$ with data $u_{0} \in H^{s}(\mathbf{R}^{2})$, $s > 1/4$. We accomplish this by improving the almost Morawetz estimates in [9].
We prove the dispersive and Strichartz estimates for solutions to the wave equation with a class of many-electric potentials in spatial dimension three. To obtain the desired dispersive estimate, based on the spectral properties of the…
With appropriate notions of Hermitian vector bundles and connections over weighted graphs which we allow to be locally infinite, we prove Feynman-Kac-type representations for the corresponding semigroups and derive several applications…
We prove two new results about the Cauchy problem for nonlinear Schroedinger equations on four-dimensional compact manifolds. The first one concerns global wellposedness for Hartree-type nonlinearities and includes approximations of cubic…
We present a class of potentials $q \colon \mathbb{R}^{n} \to (0,\infty)$ that implies the weighted Schr\"odinger semigroup $\varphi^{-1}\mathrm{e}^{-tH}\varphi$ to map a weighted Lebesgue function space…
We establish the global well-posedness of the derivative nonlinear Schr\"odinger equation with periodic boundary condition in the Sobolev space $H^{\frac12}$, provided that the mass of initial data is less than $4\pi$. This result matches…
We begin a study of a multi-parameter family of Cauchy initial-value problems for the modified nonlinear Schr\"odinger equation, analyzing the solution in the semiclassical limit. We use the inverse scattering transform for this equation,…
In recent work, two of the authors proposed a broad global well-posedness conjecture for cubic quasilinear dispersive equations in two space dimensions, which asserts that global well-posedness and scattering holds for small initial data in…