Tadele Mengesha
University of Tennessee

Localization of Nonlocal Gradients and Some Applications in Variational Convergence

Abstract
We study weighted directed difference quotients and their localization to classical notions of derivatives in several function spaces. We will characterize vector fields in the space of Sobolev spaces, space of BV functions and space of BD functions in a unified way. As an application, we will use the characterization and localization mechanism to compute Gamma limits of some nonlocal functionals that appear in application such as peridynamics.
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