Type: Seminar

Distribution: World

Expiry: 9 May 2023

CalTitle1: On an overdetermined problem involving the fractional Laplacian

Auth: sanjana@wh8hb0j3.staff.wireless.sydney.edu.au (sbha9594) in SMS-SAML

Dear friends and colleagues,
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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

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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

**Abstract:**

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

Sanjana

On behalf of Daniel H. and Ben

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Jack_thompson

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.

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