Ryan Hynd

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20112022

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15 papers · 1 filter

math.AP2020

Continuous time approximation of Nash equilibria

Romeo Awi, Ryan Hynd, Henok Mawi

We consider the problem of approximating Nash equilibria of $N$ functions $f_{1}, \dots, f_{N}$ of $N$ variables. In particular, we deduce conditions under which systems of the form $$…

math.AP2020

Extremals in nonlinear potential theory

Ryan Hynd, Francis Seuffert

We consider the PDE $- Δ_{p} u = ρ$ , where $ρ$ is a signed Borel measure on $R^{n}$ . For each $p > n$ , we characterize solutions as extremals of a generalized Morrey inequality dete…

math.AP2019

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…

math.AP2019

Asymptotic flatness of Morrey extremals

Ryan Hynd, Francis Seuffert

We study the limiting behavior as $∣ x ∣ \to \infty$ of extremal functions $u$ for Morrey's inequality on $R^{n}$ . In particular, we compute the limit of $u (x)$ as $|x|…

math.AP2019

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…

math.AP2019

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…