# 227 Gordon Palmer Hall

### Analysis Seminar – Tuoc Phan, University of Tennessee, Knoxville

227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Calderon-Zygmund theory for nonlinear partial differential equations and applications Abstract: In this talk, we will discuss several recent developments on regularity theory estimates in Sobolev spaces for solutions of several classes of elliptic and parabolic nonlinear PDEs. Some classes of considered equations may be singular and degenerate. Important ideas and techniques will be highlighted. Connections and applications of the results

### Analysis Seminar Organizational Meeting

227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United States### Analysis Seminar – Bingyuan Liu (University of California, Riverside) Geometry of the @-Neumann problem and the D{F index

227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesAbstract. We shall rst introduce the classical works of Hormander and Kohn on the L2 estimates of the @(-Neumann) problem on bounded domains and then describe applications in complex geometry. It turns out that the boundary geometry plays the fundamental role in the Sobolev estimates of the @ solution. The Diederich{Fornss index is the geometric invariant which predicts the estimates.

### Analysis Seminar – Shibin Dai (University of Alabama)

227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: An introduction to Gamma convergence Abstract: Many mathematical problems involve parameters that make those problems more and more complex or degenerate. It is of great interest to study the limiting behavior when the parameter varies. One class of such problems can be studied in a variational framework. Writing $F_\epsilpon$ as a class of functional

### Analysis Seminar

227 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United States### 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

### 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 – 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 – 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 – 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.