Wednesday, March 19, 2025 - 11:40 in V2-205
Nonlocal Boundary Value Problems with Local Boundary Conditions
A talk in the Nonlocal Equations: Analysis and Numerics series by
James Scott from New York
| 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.
Within the CRC this talk is associated to the project(s): A7 |
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