司靈得 (Daniel Spector)

Spring 2023 Nonlinear Analysis Seminar Series

*Anyone interested in the topic is welcomed to click here to access the lecture when it is being delivered.

*To view the video, click the title of each lecture.

Upcoming Events

Tuesday 28th March 2023, 3:00–4:00 pm TST (GMT+8), online on Zoom

Dominic Breit, Heriot-Watt Universiy

Title: Inclusion relations among fractional Orlicz-Sobolev spaces and a Littlewood-Paley characterization

Abstract:
Optimal embeddings among fractional Orlicz-Sobolev spaces with different smoothness are characterized. The equivalence of their Gagliardo-Slobodeckij norms to norms defined via Littlewood-Paley decompostions, via oscillations, or via Besov type difference quotients is also established. These equivalences, of independent interest, are a key tool in the proof of the relevant embeddings. This is joint work with Andrea Cianchi

Tuesday 11th April 2023, 3:00–4:00 pm TST (GMT+8), online on Zoom

Serena Dipierro, The University of Western Australia

Title: The Bernstein technique for integro-differential equations

Abstract:
In this talk we discuss how to extend the classical Bernstein technique to the setting of integro-differential operators. As a consequence of this, we are able to provide first and one-sided second derivative estimates for solutions to fractional equations. Our method is robust enough to be applied to some Pucci-type extremal equations and to obstacle problems for fractional operators.

Tuesday 18th Apr 2023, 3:00–4:00 pm TST (GMT+8), online on Zoom

Maria J. Carro, Universidad Complutense de Madrid

Title: Solving the Dirichlet and the Neumann problem at the end-point

Tuesday 25th April 2023, 3:00–4:00 pm TST (GMT+8), online on Zoom

Abhishek Ghosh, IIT Delhi

Title: TBA

Abstract: TBA

Tuesday 16th May 2023, 3:00–4:00 pm TST (GMT+8), online on Zoom

Anna Kh. Balci, Bielefeld University

Title: Behind the regularity: variational problems with energy gaps

Abstract: We study different problems with energy gaps: local and nonlocal double potential, variable exponent and weights models. We design the general procedure to construct new examples of energy gaps and present the numerical scheme that converges to the global minimiser of the problem. The talk is based on several joint projects with Lars Diening, Michail Surnachev, Johanness Srorn and Christoph Ortner.