On the wave equation with a large rough potential

2003/10/14 by Piero D'Ancona, D'Ancona, Piero, Vittoria Pierfelice +1 · 1 citation
Mathematics · #35L70 #58J45 #58J50 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA #msc:35L70 #msc:58J45 #msc:58J50

paper · pdf · doi:10.48550/arxiv.math/0310199

Major revision, corrected & augmented - 32 pages

arxiv created 2005/05/10 · arxiv updated 2009/12/01

Abstract

We prove an optimal dispersive L^∞ decay estimate for a three dimensional wave equation perturbed with a large non smooth potential belonging to a particular Kato class. The proof is based on a spectral representation of the solution and suitable resolvent estimates for the perturbed operator.

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