Friday, March 21, 2025 - 09:00 in V2-205
Variational analysis of a Dirichlet energy of half-space nonlocal gradient
A talk in the Nonlocal Equations: Analysis and Numerics series by
Xiaochuan Tian from San Diego
| Abstract: |
Inspired by recent studies in peridynamics for nonlocal mechanics, we study
variational problems associated with the half-space nonlocal gradient operator. Specifically, a Dirichlet energy involving the nonlocal gradient operator is considered. The corresponding nonlocal function space is a Hilbert
space with dense smooth functions and a nonlocal Poincare inequality.
A key result is the convergence of variational solutions as the underlying kernel functions approach a limiting form. This relies on establishing compactness results in the spirit of Bourgain, Brezis, and Mironescu.
These results lead to uniform Poincare inequalities and the convergence
of parameterized nonlocal problems, which further support the study of
asymptotically compatible Galerkin approximations.
Within the CRC this talk is associated to the project(s): A7 |
Back
