Analysis Seminar
Analysis Seminar – Khalid Said, University of Alabama
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesAbstract In this presentation we examine some useful properties of the numerical range. We explore two dierent positions , generic and generalized generic positions. We show that two pairs of subspaces (M,N) and (M?;N?) are unitarily equivalent if M and N are subspaces of Cn in generic position by constructing a unitary operator. We establish
Analysis Seminar – Simon Bortz (University of Washington)
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Sobolev contractivity of the gradient flow maximal function Abstract: In 2013, Carneiro and Svaiter showed that the heat flow maximal function is contractive in $\dot{W}^{1,2}(\mathbb{R}^n)$ for $W^{1,2}(\mathbb{R}^n)$ functions. In other words, if $K_t$ is the heat kernel then $u_*(x) = \sup_{t > 0} (K_t \ast |f|)(x)$ for some $f \in W^{1,2}(\mathbb{R}^n)$ then $\|\nabla u_*\|_{L^2(\mathbb{R}^n)}
Analysis Seminar – David Cruz-Uribe (University of Alabama)
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Matrix Ap weights, degenerate Sobolev spaces, and mappings of finite distortion of finite distortion.
Analysis Seminar – Kabe Moen (University of Alabama)
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Connections between commutators and weighted inequalities Abstract: I will cover the Cauchy integral approach to the boundedness of commutators of Calderon-Zygmund operators and BMO functions. I spoke about this approach and proved the basic commutator theorem of Coifman-Rochberg-Weiss in the fall of 2017. In this talk I will go over some powerful extensions and
Analysis Seminar – Chenchen Mou, UCLA
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Weak Solutions of Mean Field Game Master Equations. Abstract: In this talk we study master equations arising from mean field game problems, under the crucial monotonicity conditions. Classical solutions of such equations require very strong technical conditions. Moreover, unlike the master equations arising from mean field control problems, the mean field game master equations are
Analysis Seminar – Chang Yu, University of Florida
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Global solutions of the compressible Navier-Stokes equations Abstract : In this talk, I will talk about the existence of global weak solutions for the compressible Navier-Stokes equations, in particular, the viscosity coefficients depend on the density. Our main contribution is to further develop renormalized techniques so that the Mellet-Vasseur type inequality is not necessary for
Analysis Seminar – Tim Ferguson (University of Alabama)
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Bergman and Szego projections, Extremal Problems, and Square Functions Abstract: We study estimates for Hardy space norms of analytic projections. We first find a sufficient condition for the Bergman projection of a function in the unit disc to belong to the Hardy space $H^p$ for $1 < p < \infty$. We apply the result to prove
Analysis Seminar – Yuanzhen Shao (University of Alabama
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: The Fractional Porous Medium Equation on Manifolds with Conic Singularities Abstract: Due to the need to model long range diffusive interaction, during the last decade there has been a growing interest in considering diffusion equations involving non-local operators, e.g. the fractional powers of differential operators. In this talk, I will report some recent work
Analysis Seminar – Xuan Wang (University of Alabama)
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Harmonic Conjugation in Variable Exponent Harmonic Bergman Spaces Abstract: I will talk about the harmonic conjugation in variable harmonic Bergman space. In the first part of the talk, I'll provide an overview of the main result for constant exponent spaces. Then I'll illustrate our latest research on the boundedness of harmonic conjugation in variable harmonic Bergman
Analysis Seminar – Scott Rodney, Cape Breton University
346 Gordon Palmer Hall 505 Hackberry Lane, Tuscaloosa, AL, United StatesTitle: Regularity Estimates for PDE with Data in Non-Standard Spaces Abstract: In this talk I present recent joint work with D. Cruz-Uribe. Given a weak super-solution $u\in W^{1,2}_0(\Omega)$ of the elliptic equation $$-\textrm{Div}\left(Q(x)\nabla u(x) \right) = f(x)$$ in a smooth domain $\Omega$ of $\mathbb{R}^n$ with $f$ in the Birnbaum-Orlicz space $L^A(\Omega)$ ($A(t) = t^{n/2}\log^\sigma(e+t)$ with