A fractional Korn-type inequality with applications to peridynamics

Monday, October 1, 2018 - 15:00 to 16:00

Thackeray 427

Speaker Information
James Scott
University of Tennessee

Abstract or Additional Information

We show that a class of spaces of vector fields whose semi-norms involve the magnitude of “directional” difference 
quotients is in fact equivalent to the class of fractional Sobolev spaces. The equivalence can be considered a 
Korn-type characterization of fractional Sobolev spaces. We use the result to better understand the energy space 
associated to a strongly coupled system of nonlocal equations related to a nonlocal continuum model via 
peridynamics. Moreover, the equivalence permits us to apply classical Sobolev embeddings in the process of 
proving that weak solutions to the nonlocal system enjoy both improved differentiability and improved integrability.

Research Area