Recent Advances in Harmonic Analysis and Partial Differential Equations
About this Title
Andrea R. Nahmod, University of Massachusetts, Amherst, Amherst, MA, Christopher D. Sogge, Johns Hopkins University, Baltimore, MD, Xiaoyi Zhang, University of Iowa, Iowa City, IA and Shijun Zheng, Georgia Southern University, Statesboro, GA, Editors
Publication: Contemporary Mathematics
Publication Year 2012: Volume 581
ISBNs: 978-0-8218-6921-5 (print); 978-0-8218-9402-6 (online)
This volume is based on the AMS Special Session on Harmonic Analysis and Partial Differential Equations and the AMS Special Session on Nonlinear Analysis of Partial Differential Equations, both held March 12–13, 2011, at Georgia Southern University, Statesboro, Georgia, as well as the JAMI Conference on Analysis of PDEs, held March 21–25, 2011, at Johns Hopkins University, Baltimore, Maryland. These conferences all concentrated on problems of current interest in harmonic analysis and PDE, with emphasis on the interaction between them.
This volume consists of invited expositions as well as research papers that address prospects of the recent significant development in the field of analysis and PDE. The central topics mainly focused on using Fourier, spectral and geometrical methods to treat wellposedness, scattering and stability problems in PDE, including dispersive type evolution equations, higher-order systems and Sobolev spaces theory that arise in aspects of mathematical physics.
The study of all these problems involves state-of-the-art techniques and approaches that have been used and developed in the last decade. The interrelationship between the theory and the tools reflects the richness and deep connections between various subjects in both classical and modern analysis.
Graduate students and research mathematicians interested in analysis and PDE.
Table of Contents
- Aynur Bulut – The defocusing cubic nonlinear wave equation in the energy-supercritical regime
- Kevin Brewster, Irina Mitrea and Marius Mitrea – Stein's extension operator on weighted Sobolev spaces on Lipschitz domains and applications to interpolation
- T. Chen, N. Pavlović and N. Tzirakis – Multilinear Morawetz identities for the Gross-Pitaevskii hierarchy
- Xuwen Chen – Elementary Proofs for Kato Smoothing Estimates of Schrödinger-like Dispersive Equations
- Hongjie Dong and Doyoon Kim – The conormal derivative problem for higher order elliptic systems with irregular coefficients
- Marcel Filoche, Svitlana Mayboroda and Brandon Patterson – Localization of eigenfunctions of a one-dimensional elliptic operator
- Cristi Guevara and Fernando Carreon – Scattering and blow up for the two-dimensional focusing quintic nonlinear Schrödinger equation
- Christian Klein and Christof Sparber – Transverse stability of periodic traveling waves in Kadomtsev-Petviashvili equations: A numerical study
- Jeng-Eng Lin – Time Decay for the Solutions of a Fourth-Order Nonlinear Schrödinger Equation
- Ognjen Milatovic – Self-adjoint realizations of Schrödinger operators on vector bundles over Riemannian manifolds
- Irina Mitrea, Katharine Ott and Eric Stachura – Spectral properties of the reflection operator in two dimensions
- Nathan Pennington – Recent local and global solutions to the Lagrangian Averaged Navier-Stokes equation
- Chengbo Wang and Xin Yu – Recent works on the Strauss conjecture
- Dong Li and Xiaoyi Zhang – Wave operators for nonlinear wave equations with null structures
- Shijun Zheng – Fractional regularity for nonlinear Schrödinger equations with magnetic fields