All posts by medios

Continuity for maximal operators at the derivative level

Past seminar

Speaker: Cristián González Riquelme
ICTP Trieste, Italy

Date: January 6, 2022 at 16:15 Santiago time

Abstract: Maximal operators are central objects in harmonic analysis. The oscillatory behavior of such objects has been an important topic of study over the last decades. However, even in the dimension one there are interesting questions that remain open. In this talk we will discuss recent developments and open questions about this topic, particularly about the boundedness and continuity for such operators at the derivative level.

Venue: Online via Zoom
Chair: Claudio Muñoz

YouTube video (in Spanish)

 

The fibering method applied to the level sets of a family of functionals

Past seminar

Speaker: Kaye Silva
Universidade Federal de Goiás, Brazil

Date: December 16, 2021 at 16:15 Santiago time

Abstract:  Given an one-parameter family of C1-functionals, Φμ : X →R, defined on an uniformly convex Banach space X, we describe a method that permit us find critical points of Φμ at some energy level c ∈ R. In fact, we show the existence of a sequence μ(n,c), n ∈N, such that Φμ(n,c) has a critical level at c ∈ R, for all n ∈ N. Moreover, we show some good properties of the curves μ(n,c), with respect to c (for example, they are Lipschitz), and as a consequence of this analysis, we recover many know results on the literature concerning bifurcations of elliptic partial differential equations. Furthermore we prove new results for a large class of elliptic partial differential equations, which includes, for example, Ouyang, Lane-Enden, Concave-Convex, Kirchhoff and Schrödinger-Bopp-Podolsky type equations.

Venue: Online via Zoom
Chair: Gabrielle Nornberg

YouTube video (in English)

 

 

Maximal function estimates and local well-posedness for the generalized Zakharov–Kuznetsov equation

Past seminar

Speaker: Felipe Linares
IMPA, Brazil

Date: December 9, 2021 at 16:15 Santiago time

Abstract: In this talk we will discuss recent results regarding local well-posedness for the generalized Zakharov–Kuznetsov equation. We prove a high-dimensional version of the Strichartz estimates for the unitary group associated with the free Zakharov-Kuznetsov equation. As a by-product, we deduce maximal estimates which allow us to prove local well-posedness for the generalized Zakharov-Kuznetsov equation in the whole subcritical case whenever d\ge 4, k\ge 4 complementing the recent results of Kinoshita and Herr-Kinoshita. Finally, we use some of those maximal estimates in order to prove pointwise convergence results for the flow of the generalized Zakharov–Kuznetsov equation in any dimension, in the same spirit of a recent manuscript by Compaan, Lucà and Staffilani.

Venue: Online via Zoom / Sala de seminarios DIM, Beauchef 851, piso 5
Chair: Claudio Muñoz

YouTube video (in English)