We prove that certain boundedness properties of operators yield distributional estimates that have exponential decay at infinity. Such distributional estimates imply local exponential integrability and apply to many operators such as m-linear Calderón-Zygmund operators and their maximal counterparts.

We consider manifolds with conic singularites that are isometric to R outside a compact set. Under natural geometric assumptions on the cone points, we prove the existence of a logarithmic resonancefree region for the cut-off resolvent. The estimate also applies to the exterior domains of non-trapping polygons via a doubling process. The proof of the resolvent estimate relies on the propagation...

We consider the wave equation in an unbounded conical domain, with initial conditions and boundary conditions of Dirichlet or Neumann type. We give a uniform decay estimate of the solution in terms of weighted Sobolev norms of the initial data. The decay rate is the same as in the full space case.

We consider the amplitude decay for the linearized equations governing irrotational vortex sheets and water waves with surface tension. Using oscillatory integral estimates, we prove that the magnitude of the amplitude decays faster than t−1/3.

This article concerns the stabilization for a well-known Lienard’s system of ordinary differential equations modelling oscillatory phenomena. It is known that such a system is asymptotically stable when a linear viscous (motion-activated) damping with constant gain is engaged. However, in many applications it seems more realistic that the aforementioned gain is not constant and does depend on t...

In this article we consider variable coefficient, time dependent wave equations in exterior domains R × (R \ Ω), n ≥ 3. We prove localized energy estimates if Ω is star-shaped, and global in time Strichartz estimates if Ω is strictly convex.

In this paper the time decay rates for the solutions to the Schr odinger–Poisson system in the repulsive case are improved in the context of semiconductor theory. Upper and lower estimates are obtained by using a norm involving the potential energy and the dispersion equation. In the attractive case some examples, based on the Galilean invariance, are proposed showing that the solutions does no...

We establish weighted L2−estimates for dissipative wave equations with variable coefficients that exhibit a dissipative term with a space dependent potential. These results yield decay estimates for the energy and the L2−norm of solutions. The proof is based on the multiplier method where multipliers are specially engineered from asymptotic profiles of related parabolic equations.

In this paper we use a unified way studying the decay estimate for a class of dispersive semigroup given by eitφ( √ −∆), where φ : R+ → 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.