4 papers · 1 filter
On the symmetry and monotonicity of Morrey extremals
Ryan Hynd, Francis Seuffert
We employ Clarkson's inequality to deduce that each extremal of Morrey's inequality is axially symmetric and is antisymmetric with respect to reflection about a plane orthogonal to…
Asymptotic flatness of Morrey extremals
Ryan Hynd, Francis Seuffert
We study the limiting behavior as of extremal functions for Morrey's inequality on . In particular, we compute the limit of as $|x|…
A trajectory map for the pressureless Euler equations
Ryan Hynd
We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles…
Lagrangian coordinates for the sticky particle system
Ryan Hynd
The sticky particle system is a system of partial differential equations which assert the conservation of mass and momentum of a collection of particles that interact only via inel…