相关论文: Spectral Theory and Nonlinear PDE: a Survey
This is a survey on spectral theory of dynamical systems.
This is to review some recent progress in PDE. The emphasis is on (energy) supercritical nonlinear Schr\"odinger equations. The methods are applicable to other nonlinear equations.
Expanded lecture notes. Preliminary version, comments are welcome.
This survey is a 2022 update of the 2008 version, with recent developments and new references.
This paper surveys and discusses recent work adapting partial differential equation (PDE) models to discrete structures.
This is a survey of noncommutative generalizations of the spectrum of a ring, written for the Notices of the American Mathematical Society.
THis work is a survey of a few nonlinear PDE based models in image restoring.
This is a survey of the spectral theory of tensors.
We present a short review of the evolution of the methodology of the Method of simplest equation for obtaining exact particular solutions of nonlinear partial differential equations (NPDEs) and the recent extension of a version of this…
This survey deals with the construction of a category of spectral triples that is compatible with the Kasparov product in $KK$-theory. These notes serve as an intuitive guide to these results, avoiding the necessary technical proofs. We…
In this survey, we give a short overview of the recent progress on the multidimensional L2 conjecture. It can also serve as an introduction to the subject.
This is a survey on rectifiability. I discuss basic properties of rectifiable sets, measures, currents and varifolds and their role in complex and harmonic analysis, potential theory, calculus of variations, PDEs and some other topics.
This paper is a survey on Deduction modulo theory
We correct some oversights in the paper "A spectral sequence for stratified spaces and configuration spaces of points" by the second named author. In particular we explain that an additional hypothesis should be added to Theorem 4.15 in…
In this revised version, we add some expository material and references and make some minor corrections.
Explicit expression for quasi-triviality of scalar non-linear PDE is under consideration.
We survey noncommutative Choquet theory and some of its applications.
This is a survey paper of Shelah's pcf theory. In this part the theory is developed up to the pcf theorem.
This is a survey work on Lie algebras with ad-invariant metrics. We summarize main features, notions and constructions, in the aim of bringing into consideration the main research on the topic. We also give some list of examples in low…
The aim of this work is to give an overview of the recent developments in the area of statistical inference for parabolic stochastic partial differential equations. Significant part of the paper is devoted to the spectral approach, which is…