Cutoff Resolvent Estimates and the Semilinear Schrödinger Equation

2007/06/28 by Hans Christianson, Christianson, Hans
Mathematics · #35G25 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math.AP #msc:35G25

paper · pdf · doi:10.48550/arxiv.0706.4315

8 pages, 1 figure

openalex publication_date 2007/06/28 · arxiv created 2007/11/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper shows how abstract resolvent estimates imply local smoothing for solutions to the Schrödinger equation. If the resolvent estimate has a loss when compared to the optimal, non-trapping estimate, there is a corresponding loss in regularity in the local smoothing estimate. As an application, we apply well-known techniques to obtain well-posedness results for the semi-linear Schrödinger equation.

Citations

• Sharp Strichartz estimates on non-trapping asymptotically conic\n manifolds

Related

• On the Local Smoothing for the Schroedinger Equation
• Local smoothing for the Schrödinger equation with a prescribed loss
• Local Smoothing Estimates near a Trapped Set with Infinitely Many Connected Components
• Resolvent estimates with mild trapping
• Dispersive estimates for wave and Schrödinger equations with a potential in non-trapping exterior domains