5 papers · 1 filter
Lipschitz regularity for a homogeneous doubly nonlinear PDE
Ryan Hynd, Erik Lindgren
We study the doubly nonlinear PDE This equation arises in the study of extremals of Poincaré ineq…
Newton's second law with a semiconvex potential
Ryan Hynd
We make the elementary observation that the differential equation associated with Newton's second law always has a solution for given initial conditions pro…
Extremal functions for Morrey's inequality
Ryan Hynd, Francis Seuffert
We give a qualitative description of extremals for Morrey's inequality. Our theory is based on exploiting the invariances of this inequality, studying the equation satisfied by ext…
Probability measures on the path space and the sticky particle system
Ryan Hynd
We study collections of point masses which move freely along the real line and stick together when they collide via perfectly inelastic collisions. We quantify the way particles st…
Sticky particles and the pressureless Euler equations in one spatial dimension
Ryan Hynd
We consider the dynamics of finite systems of point masses which move along the real line. We suppose the particles interact pairwise and undergo perfectly inelastic collisions whe…