171 research outputs found
Principal eigenvalue of the fractional Laplacian with a large incompressible drift
We add a divergence-free drift with increasing magnitude to the fractional
Laplacian on a bounded smooth domain, and discuss the behavior of the principal
eigenvalue for the Dirichlet problem. The eigenvalue remains bounded if and
only if the drift has non-trivial first integrals in the domain of the
quadratic form of the fractional Laplacian.Comment: 19 page
Recommended from our members
Mini-Workshop: Mathematical Analysis for Peridynamics
A mathematical analysis for peridynamics, a nonlocal elastic theory, is the subject of the mini-workshop. Peridynamics is a novel multiscale mechanical model where the canonical divergence of the stress tensor is replaced by an integral operator that sums forces at a finite distance. As such, the underlying regularity assumptions are more general, for instance, allowing discontinuous and non-differentiable displacement fields. Although the theoretical mechanical formulation of peridynamics is well understood, the mathematical and numerical analyses are in their early stages. The mini-workshop proved to be a catalyst for the emerging mathematical analyses among an international group of mathematicians
- …