Analysis Seminar
Seminar – Francesco Di Plinio, University of Virginia
227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Sparse domination of singular integral operators. Abstract: Singular integral operators, which are a priori signed and non-local, can be dominated in norm, pointwise, or dually, by sparse averaging operators, which are in contrast positive and localized. The most striking consequence is that weighted norm inequalities for the singular integral follow from the corresponding, rather
Analysis Seminar – Oscar Guzman, Departamento de Matematicas, Universidad Nacional de Colombia, Bogota, Colombia
227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesVARIABLE EXPONENT BOUNDED VARIATION SPACES IN THE RIESZ SENSE Abstract This talk introduces Variable Exponent Bounded Variation Spaces in the Riesz Sense. We prove some embedding results and present a Riesz representation lemma in our setting . Also it shows an application of the latter result by characterizing the global Lipschitz Nemytskii operator on the newly introduced spaces
Analysis Seminar – Michael Dabkowski (Lawrence Technological University)
227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Global Stability of a Class of Nonlinear PDE with a Nonlocal Term Abstract: We will establish global asymptotic stability results for a class of non-linear PDE which arise in approximations of models of particle coarsening. These PDE must satisfy a conservation of mass constraint which induces a nonlocal term into the equation. Our method
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.