IVANOVICI , Oana

The purpose of this note is to prove dispersive estimates for the wave equation outside a ball in R^d. If d = 3, we show that the linear flow satisfies the dispersive estimates as in R^3. In higher dimensions d ≥ 4 we show that losses in dispersion do appear and this happens at the Poisson spot.

We consider the wave and Schrödinger equations with Dirichlet boundary conditions in the exterior of a ball in $R^d$. In dimension $d = 3$ we construct a sharp, global in time parametrix and then proceed to obtain sharp dispersive estimates, matching the $R^3$ case, for all frequencies (low and high). If $d ≥ 4$, we provide an explicit solution...

We consider the wave and Schrödinger equations with Dirichlet boundary conditions in the exterior of a ball in $R^d$. In dimension $d = 3$ we construct a sharp, global in time parametrix and then proceed to obtain sharp dispersive estimates, matching the $R^3$ case, for all frequencies (low and high). If $d ≥ 4$, we provide an explicit solution...

We prove better Strichartz type estimates than expected from the (optimal) dispersion we obtained in our earlier work on a 2d convex model. This follows from taking full advantage of the space-time localization of caustics in the parametrix we obtain, despite their number increasing like the inverse square root of the distance from the source...

We consider a model case for a strictly convex domain of dimension $d\geq 2$ with smooth boundary and we describe dispersion for the wave equation with Dirichlet boundary conditions. More specifically, we obtain the optimal fixed time decay rate for the smoothed out Green function: a $t^{1/4}$ loss occurs with respect to the boundary less case,...

We consider a model case for a strictly convex domain of dimension $d\geq 2$ with smooth boundary and we describe dispersion for the wave equation with Dirichlet boundary conditions. More specifically, we obtain the optimal fixed time decay rate for the smoothed out Green function: a $t^{1/4}$ loss occurs with respect to the boundary less case,...

We prove sharper Strichartz estimates than expected from theoptimal dispersion bounds.

We prove that the range of Strichartz estimates on a model 2D convex domain may be further restricted compared to the known counterexamples due to the first author. Our new family of counterexamples is now built on the parametrix construction from our earlier work. Interestingly enough, it is sharp in at least some regions of phase space.

We consider the wave equation on a strictly convex domain of dimension at least two with smooth non empty boundary and with Dirichlet boundary conditions. We construct a sharp local in time parametrix and then proceed to obtain dispersion estimates: our fixed time decay rate for the Green function exhibits a $t^{1/4}$ loss with respect to the...