Calculus of Variations and Geometric Measure Theory

L'operatore d'onda a coefficienti variabili in dimensione 1

Piero D'Ancona (Dip. Mat. Univ. Roma ``La Sapienza'')

created by alberti on 11 Nov 2005
modified on 14 Nov 2005

16 nov 2005

Abstract.

Seminario di Analisi Analysis seminar

when: Wednesady, November 16, at 16 pm

where: Dipartimento di Matematica, Sala Riunioni

speaker: Piero D'Ancona (Università di Roma I)

title: The wave operator with variable coefficients in dimension 1

abstract: The wave operator intertwines the perturbed Schroedinger operator $-\Delta+V(x)$ with the free operator $-\Delta$. This allows to extend many results from the free to the perturbed case. In particular, by proving the $L^p$ boundeness of the wave operator one gets as immediate consequences the decay estimates for a number of evolution equations with variable coefficients (waves, heat, Schroedinger). Recently, in a joint work with L. Fanelli we have obtained new results about the $L^p$ boundeness of the one-dimensional wave operator with variable coeffcients, improving previous results of Artbazar-Yajima and Weder. We believe that our results are optimal from the point of view of the regularity of coefficients.