Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userImproved time-decay for a class of scaling critical electromagnetic Schrodinger flows
244
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We consider a Schrodinger hamiltonian $H(A,a)$ with scaling critical and time independent external electromagnetic potential, and assume that the angular operator $L$ associated to $H$ is positive definite. We prove the following: if $|e^{-itH(A,a)}|_{L^1to L^infty}lesssim t^{-n/2}$, then $ ||x|^{-g(n)}e^{-itH(A,a)}|x|^{-g(n)}|_{L^1to L^infty}lesssim t^{-n/2-g(n)}$, $g(n)$ being a positive number, explicitly depending on the ground level of $L$ and the space dimension $n$. We prove similar results also for the heat semi-group generated by $H(A,a)$.
rate research
Read More
We construct a local in time, exponentially decaying solution of the one-dimensional variable coefficient Schrodinger equation by solving a nonstandard boundary value problem. A main ingredient in the proof is a new commutator estimate involving the projections P+ and P- onto the positive and negative frequencies.
We prove Rellich and improved Rellich inequalities that involve the distance function from a hypersurface of codimension $k$, under a certain geometric assumption. In case the distance is taken from the boundary, that assumption is the convexity of the domain. We also discuss the best constant of these inequalities.
We prove two improv
We consider the inverse problem of determining the time and space dependent electromagnetic potential of the Schrodinger equation in a bounded domain of $mathbb R^n$, $ngeq 2$, by boundary observation of the solution over the entire time span. Assuming that the divergence of the magnetic potential is fixed, we prove that the electric potential and the magnetic potential can be Holder stably retrieved from these data, whereas stability estimates for inverse time-dependent coefficients problems of evolution partial differential equations are usually of logarithmic type.
In this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by $e^{itphi(sqrt{-Delta})}$, where $phi: mathbb{R}^+to mathbb{R}$ is smooth away from the origin. Especially, the decay estimates for the solutions of the Klein-Gordon equation and the beam equation are simplified and slightly improved.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
