Extremal functions for Morrey's inequality
Ryan Hynd, Francis Seuffert
TL;DR
This paper characterizes the extremal functions for Morrey's inequality by analyzing their invariances, the differential equations they satisfy, and their relation to a convex minimization problem.
Contribution
It provides a qualitative description of extremals for Morrey's inequality, linking invariance properties and optimality conditions.
Findings
Extremals are characterized through invariance analysis.
Extremals satisfy a specific differential equation.
Extremals are solutions to a related convex minimization problem.
Abstract
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 extremals and the observation that extremals are optimal for a related convex minimization problem.
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