Related papers: Carleman estimate on a tree for Schrodinger equati…
We prove a sharp, global-in-time Strichartz estimate for the Schr\"odinger equation on the cylinder $\mathbb{R}\times\mathbb{T}$.
This paper concerns about the weak unique continuation property of solutions of a general system of differential equation/inequality with a second order strongly elliptic system as its leading part. We put not only some natural assumption…
In a series of publications of the second author, including some with coauthors, globally strictly convex Tikhonov-like functionals were constructed for some nonlinear ill-posed problems. The main element of such a functional is the…
In this paper, we establish a weight identity for stochastic beam equation by means of the multiplier method. Based on this identity, we first establish the global Carleman estimate for the special system with zero initial value and end…
A refinement of uniform resolvent estimate is given and several smoothing estimates for Schrodinger equations in the critical case are induced from it. The relation between this resolvent estimate and radiation condition is discussed. As an…
Using Carleman estimates, we give a lower bound for solutions to the discrete Schr\"odinger equation in both dynamic and stationary settings that allows us to prove uniqueness results, under some assumptions on the decay of the solutions.
We prove global smoothing and Strichartz estimates for the Schroedinger, wave, Klein-Gordon equations and for the massless and massive Dirac systems, perturbed with singular electromagnetic potentials. We impose a smallness condition on the…
In this article, we establish scale-invariant Strichartz estimates for the Schr\"odinger equation on arbitrary compact globally symmetric spaces and some bilinear Strichartz estimates on products of rank-one spaces. As applications, we…
A one-dimensional generalized nonlinear Schroedinger equation is considered, and the corresponding inverse scattering problem is analyzed when the potential is compactly supported and depends on the wave function. The unique recovery of the…
This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…
A recognized trend of research investigates generalizations of the Hadamard's inversion theorem to functions that may fail to be differentiable. In this vein, the present paper explores some consequences of a recent result about the…
We establish new intrinsic Strichartz estimates for solutions of the Cauchy problem for a class of possibly degenerate Schr\"odinger equations with a real drift.
We prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof which is essentially based…
We consider a time-dependent structured population model equation and establish a Carleman estimate. We apply the Carleman estimate to prove the unique continuation which means that Cauchy data on any lateral boundary determine the solution…
We prove in this paper the global Lorentz estimate in term of fractional-maximal function for gradient of weak solutions to a class of p-Laplace elliptic equations containing a non-negative Schr\"odinger potential which belongs to reverse…
In this article, We investigate an inverse problem of determining the time-dependent source factor in parabolic integro-differential equations from boundary data. We establish the uniqueness and the conditional stability estimate of…
The inverse problem of estimating dielectric constants of explosives using boundary measurements of one component of the scattered electric field is addressed. It is formulated as a coefficient inverse problem for a hyperbolic differential…
In this paper, we establish an optimal dual version of trace estimate involving angular regularity. Based on this estimate, we get the generalized Morawetz estimates and weighted Strichartz estimates for the solutions to a large class of…
In this work we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, we show that the ill-posedness decreases when we…
In this note we give a proof-by-formula of certain important embedding inequalities on dyadic tree. This is done with the help of Bellman function. We also consider the case of a bi-tree, where a different approach is explained.