𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Local smoothing for Kato potentials in three dimensions

✍ Scribed by J. A. Barceló; J.M. Bennett; A. Ruiz; M. C. Vilela

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
194 KB
Volume
282
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We prove weighted local smoothing estimates for the resolvent of the Laplacian in three dimensions with weights belonging to the Kerman–Sawyer class. This class contains the well‐known global Kato and Rollnik classes. We go on to discuss dispersive and Strichartz estimates for perturbations of the Laplacian by small potentials, and apply our results and observations to the well‐posedness in L^2^ of the Cauchy problem for some linear and semilinear Schrödinger equations (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Vector potentials in three-dimensional n
Vector potentials in three-dimensional non-smooth domains
✍ C. Amrouche; C. Bernardi; M. Dauge; V. Girault 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 294 KB

This paper presents several results concerning the vector potential which can be associated with a divergence-free function in a bounded three-dimensional domain. Different types of boundary conditions are given, for which the existence, uniqueness and regularity of the potential are studied. This i

High-order corrected trapezoidal quadrat
High-order corrected trapezoidal quadrature rules for the coulomb potential in three dimensions
✍ J.C. Aguilar; Yu Chen 📂 Article 📅 2005 🏛 Elsevier Science 🌐 English ⚖ 387 KB

We construct correction coefficients for high-order trapezoidal quadrature rules to evaluate three-dimensional singular integrals of the form, where the domain D is a cube containing the point of singularity (0, 0, 0) and v is a C °o function defined on R 3. The procedure employed here is a general