Date
Thu, 26 Apr 2018
Time
12:00 - 13:00
Location
L4
Speaker
Florian Schweiger
Organisation
University of Bonn

We consider the discrete Bilaplacian on a cube in two and three dimensions with zero boundary data and prove estimates for its Green's function that are sharp up to the boundary. The main tools in the proof are Caccioppoli estimates and a compactness argument which allows one to transfer estimate for continuous PDEs to the discrete setting. One application of these estimates is to understand the so-called membrane model from statistical physics, and we will outline how these estimates can be applied to understand the phenomenon of entropic repulsion. We will also describe some connections to numerical analysis, in particular another approach to these estimates based on convergence estimates for finite difference schemes.

Please contact us with feedback and comments about this page. Last updated on 04 Apr 2022 14:57.