SMS scnews item created by Sanjana Bhardwaj at Mon 8 May 2023 0929
Type: Seminar
Distribution: World
Expiry: 9 May 2023
Calendar1: 8 May 2023 1500-1600
CalLoc1: Zoom webinar
CalTitle1: On an overdetermined problem involving the fractional Laplacian
Auth: (sbha9594) in SMS-SAML

Asia-Pacific Analysis and PDE Seminar

On an overdetermined problem involving the fractional Laplacian

Jack Thompson

Dear friends and colleagues,   
on Monday, 8 May 2023 at
  • 1:00 PM for Beijing, Hong Kong and Perth
    • 02:00 PM for Seoul and Tokyo
  03:00 PM for Canberra, Melbourne and Sydney
05:00 PM for Auckland

PhD Candidate Jack Thompson is giving a talk in our Asia-Pacific Analysis and  PDE Seminar on   

On an overdetermined problem involving the fractional Laplacian


Overdetermined problems are a type of boundary value problem where `too many' conditions are imposed on the solution. In general, such a problem is ill-posed, so the main objective is to classify sets in which the problem is well-posed. A classical result due to J. Serrin says that a bounded domain in \$\mathbb R^n$ that admits a function with constant Laplacian, zero Dirichlet data, and constant Neumann data must be a ball. We consider a semi-linear generalisation of Serrin's problem driven by the fractional Laplacian where the value of the solution is prescribed on surface parallel to the boundary. We prove that the existence of a non-negative solution forces the region to be a ball. We also discuss some further related results. This is joint work with S. Dipierro, G. Poggesi, and E. Valdinoci.

Chair: Enrico Valdinoci (Professor @ University of Western Australia)

More information and how to attend this talk can be found at the seminar webpage

On behalf of Daniel H. and Ben


Webinar Speaker

PhD candidate @ University of Western Australia

He is a PhD candidate in the Department of Mathematics and Statistics at the University of Western Australia, supervised by Enrico Valdinoci, Serena Dipierro, and Lyle Noakes. My research interests are in elliptic/parabolic partial differential equations, particularly in integro-differential equations. Currently, he is working on projects in nonlocal overdetermined problems and regularity theory for nonlocal elliptic PDE.