F. Seuffert

activity

20182020

collaborators

4 papers

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.AP2018

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…