The \infty eigenvalue problem and a problem of optimal transportation

The so-called eigenvalues and eigenfunctions of the infinite Laplacian $\Delta_\infty$ are defined through an asymptotic study of that of the usual $p$-Laplacian $\Delta_p$, this brings to a characterization via a non-linear eigenvalue problem for a PDE satisfied in the viscosity sense. In this paper, we obtain an other characterization of the first eigenvalue via a problem of optimal transportation, and recover properties of the first eigenvalue and corresponding positive eigenfunctions

Experimental study of radiative shocks at PALS facility

We report on the investigation of strong radiative shocks generated with the high energy, sub-nanosecond iodine laser at PALS. These shock waves are characterized by a developed radiative precursor and their dynamics is analyzed over long time scales (~50 ns), approaching a quasi-stationary limit. We present the first preliminary results on the rear side XUV spectroscopy. These studies are relevant to the understanding of the spectroscopic signatures of accretion shocks in Classical T Tauri Stars.Comment: 21 pages, 1 table, 7 figure