Speaker: James Scott (Auburn University)

 

Title: Nonlocal Boundary Value Problems with Local Boundary Conditions

 

 

Abstract: We state and analyze nonlocal problems with classically-defined, local boundary conditions. The model takes its horizon parameter to be spatially dependent, vanishing near the boundary of the domain. We establish a Green's identity for the nonlocal operator that recovers the classical boundary integral, which permits the use of variational techniques. Using this, we show the existence of weak solutions, as well as their variational convergence to classical counterparts as the bulk horizon parameter uniformly converges to zero. In certain circumstances, global regularity of solutions can be established, resulting in improved modes and rates of variational convergence. Generalizations of these results pertaining to models in continuum mechanics and Laplacian learning will also be presented.

 

 

Host: Yuming Paul Zhang

 

 

ACM seminar’s website: https://sites.google.com/view/yzhangpaul/applied-and-computational-mathematics-seminars