ﻻ يوجد ملخص باللغة العربية
In this paper, we prove a limiting absorption principle for high-order Schrodinger operators with a large class of potentials which generalize some results by A. Ionescu and W. Schlag. Our main idea is to handle the boundary operators by the restriction theorem of Fourier transform. Two key tools we use in this paper are the Stein--Tomas theorem in Lorentz spaces and a sharp trace lemma given by S. Agmon and L. Hormander
We use a Lagrangian perspective to show the limiting absorption principle on Riemannian scattering, i.e. asymptotically conic, spaces, and their generalizations. More precisely we show that, for non-zero spectral parameter, the `on spectrum, as well
We establish a limiting absorption principle for some long range perturbations of the Dirac systems at threshold energies. We cover multi-center interactions with small coupling constants. The analysis is reduced to study a family of non-self-adjoint
In this paper we prove some multi-linear Strichartz estimates for solutions to the linear Schrodinger equations on torus $T^n$. Then we apply it to get some local well-posed results for nonlinear Schrodinger equation in critical $H^{s}(T^n)$ spaces.
We establish that trace inequalities $$|D^{k-1}u|_{L^{frac{n-s}{n-1}}(mathbb{R}^{n},dmu)} leq c |mu|_{L^{1,n-s}(mathbb{R}^{n})}^{frac{n-1}{n-s}}|mathbb{A}[D]u|_{L^{1}(mathbb{R}^{n},dmathscr{L}^{n})}$$ hold for vector fields $uin C^{infty}(mathbb{R}^{
We study the wellposedness of Cauchy problem for the fourth order nonlinear Schrodinger equations ipartial_t u=-epsDelta u+Delta^2 u+P((partial_x^alpha u)_{abs{alpha}ls 2}, (partial_x^alpha bar{u})_{abs{alpha}ls 2}),quad tin Real, xinReal^n, where $e