Speaker: Serena Dipierro, University of Western Australia

Time : 10:00 - 11:00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

Zoom : A Zoom link will appear here, an hour before the talk

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Mean Value Theorem, Malmheden Theorem, fractional Laplacian

Abstract:  We present a classical result by Malmheden based on a simple algorithm to determine the harmonic function in a ball, and we discuss the fractional counterpart, from which one obtains a representation formula for s-harmonic functions as a linear superposition of weighted classical harmonic functions and a new simple proof of the fractional Harnack inequality.

Biography: Serena Dipierro took her PhD in Mathematical Analysis at the International School for Advanced Studies (SISSA, Trieste) in 2012. After PostDoc positions at the Universidad de Chile and University of Edinburgh, and a Humboldt Fellowship, she held permanent positions at the University of Melbourne and the Università di Milano. In August 2018 she moved at the University of Western Australia, where she is now Professor of Mathematics.

Serena is Fellow of the Australian Mathematical Society, and Australian Mathematical Society Hanna  Neumann Lecturer. She has obtained prestigious awards, including the Australian Mathematical Society Medal, the Mahony-Neumann-Room Prize, the Bartolozzi Prize of the Italian Mathematical Union, the  Christopher Heyde Medal of the Australian Academy of Science, and the Prize of the Bulletin of the Brazilian Mathematical Society.

Bibliography

[1] Dipierro, Serena; Valdinoci, Enrico, Elliptic partial differential equations from an elementary viewpoint - a fresh glance at the classical theory. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, (2024) xvii+651 pp.

[2] Bucur, Claudia; Dipierro, Serena; Valdinoci, Enrico, On the mean value property of fractional harmonic functions. Nonlinear Anal. 201 (2020), 112112, 25 pp.