Details

Autor(en) / Beteiligte

• Christianson, Hans
• Wunsch, Jared

Titel

LOCAL SMOOTHING FOR THE SCHRÖDINGER EQUATION WITH A PRESCRIBED LOSS

Ist Teil von

• American journal of mathematics, 2013-12, Vol.135 (6), p.1601-1632

Ort / Verlag

Baltimore: Johns Hopkins University Press

Erscheinungsjahr

2013

Quelle

Project MUSE

Beschreibungen/Notizen

• We consider a family of surfaces of revolution, each with a single periodic geodesic which is degenerately unstable. We prove a local smoothing estimate for solutions to the linear Schrödinger equation with a loss that depends on the degeneracy, and we construct explicit examples to show our estimate is saturated on a weak semiclassical time scale. As a byproduct of our proof, we obtain a cutoff resolvent estimate with a sharp polynomial loss.