Dispersive Estimates for Manifolds with One Trapped Orbit
نویسندگان
چکیده
منابع مشابه
Dispersive Estimates for Manifolds with One Trapped Orbit
For a large class of complete, non-compact Riemannian manifolds, (M, g), with boundary, we prove high energy resolvent estimates in the case where there is one trapped hyperbolic geodesic. As an application, we have the following local smoothing estimate for the Schrödinger propagator:
متن کاملDispersive estimates for Schrödinger operators in dimensions one and three
A “resonance” here is defined to take place iff W (0) = 0 where W (λ) is the Wronskian of the two Jost solutions at energy λ2, see the following section. It is known that the spectrum of H is purely absolutely continuous on (0,∞) under our assumptions (V ∈ L1(R) suffices for that) so that Pac is the same as the projection onto the orthogonal complement of the bound states. For the case of three...
متن کاملTwo-orbit Manifolds with Boundary
In this article we are interested in the classification of some Lie group actions on differentiable manifolds. In full generality, classifying all actions of Lie groups is of course an unachievable task. Let us consider the case when there are very few orbits. The case of transitive actions is easily dealt with: the manifold is then a homogeneous space, and it is sufficient to give the stabiliz...
متن کاملDispersive Estimates, Strichartz Estimates and Smoothing Effects
In this short expository note, we will discuss three subjects: dispersive estimates, Strichartz estimates and smoothing effects which are of great importance in the study of dispersive equations. We will focus on the Euclidean setting and try to derive the interplay among above three objects. We will mainly focus on linear problems in various contexts. Some nonlinear application will also be me...
متن کاملDispersive Estimates for a Linear Wave Equation with Electromagnetic Potential
We consider radial solutions to the Cauchy problem for a linear wave equation with a small short-range electromagnetic potential (depending on space and time) and zero initial data. We present two dispersive estimates that provide, in particular, an optimal decay rate in time t−1 for the solution. Also, we apply these estimates to obtain similar results for the linear massless Dirac equation pe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2008
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605300802133907