Analysis Seminar
Analysis Seminar
227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesAnalysis Seminar – Eduard Roure Perdices, Universidad de Barcelona
227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Weighted restricted weak type inequalities Abstract: We review classical results concerning the bounds of the Hardy-Littlewood maximal operator on weighted Lorentz spaces and discuss the analogous bounds for the pointwise product of such operators. A new Hölder-type inequality for Lorentz spaces is used.
Analysis Seminar – Hyun Kwon, University of Alabama
227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Cowen-Douglas Operators and the Corona Problem Abstract: I will discuss how the recent method used in solving various form of the corona problem can be used to classify Cowen-Douglas operators up to similarity.
Analysis Seminar – John-Oliver MacLellan (University of Alabama)
227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: "A Compact Embedding Theorem for Degenerate Sobolev Spaces" Abstract: In this talk I will prove a compact embedding theorem for degenerate Sobolev spaces into naturally associated weighted Lebesgue spaces. This is a generalization of the Rellich Kondrachov compactness theorem for classical Sobolev spaces. These embeddings have been studied in a very general context in
Analysis Seminar – Arum Lee (University of Alabama)
227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Definition of Weak Solution of Poisson Equation with Homogeneous Dirichlet Boundary Condition Abstract: In this talk, I will discuss the ideas of weak derivatives, traces of Sobolev functions and the weak solution of Poisson equation. These definitions are the very basic but important definitions in PDE. This talk will explain the motivation behind these
Analysis Seminar – Yuanzhen Shao, Georgia Southern University
227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Some Applications of Singular Manifold Theory to Applied Mathematics Abstract: Many applications of applied sciences lead to differential equations with various types of singularities, including singularities of the geometry of the underlying space and singularities of the coefficients of the differential equations. The aim of this talk is to introduce the concept of singular manifolds, which can describe various kinds of singularities in a unified way, and then my recent work on the partial differential equation theory over singular manifolds will be presented. I will illustrate by several examples from applied mathematics how to use this theory to treat different types of singularities via a unified approach.
Analysis Seminar – Oleksandra Beznosova (University of Alabama)
227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: The star discrepancy conjecture Abstract: We will discuss theoretical and computational aspects of the star discrepancy in dimension 3 and above.
Analysis Seminar – Ollie Tapiola (University of Missouri)
227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Carleson measures, uniform wrectifiability and $\varepsilon$-approximability of harmonic functions in $L^p$ Abstract: Uniform rectifiability is a geometric property that is strongly connected with harmonic analysis and elliptic PDE. Although many powerful PDE tools are not available in spaces with uniformly rectifiable boundaries, several authors have recently managed to prove positive PDE results in this
Analysis Seminar – Xiangsheng Xu (Mississippi State University)
227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesLogarithmic up bounds for weak solutions to a class of parabolic equations 2.23.18 abstract
Analysis Seminar – David Cruz-Uribe (University of Alabama)
227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Poincare inequalities and Neumann problems for the p-Laplacian Abstract: I will discuss my recent work with Scott Rodney on the following equivalence: the existence of solutions to a degenerate p-Laplacian equation and the existence of a weighted (p,p) Poincare inequality. Our results are in the context of degenerate Sobolev spaces, where the degeneracy is