S. MacDonald

activity

20222026

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math.FA2023

Sum of Squares Decompositions in Hölder Spaces

Sullivan Francis MacDonald

We investigate the number of half-regular squares required to decompose a non-negative $C^{k, α} (R^{n})$ function into a sum of squares. Each non-negative $C^{3,1}(\mathbb{R}…

math.AP2023

Regularity of Singular Solutions to $p$ -Poisson Equations

Sullivan Francis MacDonald

This work showcases level set estimates for weak solutions to the $p$ -Poisson equation on a bounded domain, which we use to establish Lebesgue space inclusions for weak solutions.…

math.FA2023

Regularity Preserving Sum of Squares Decompositions

Sullivan F. MacDonald

In the process of proving a sharpened form of Gårding's inequality, Fefferman & Phong demonstrated that every non-negative function $f \in C^{3, 1} (R^{n})$ can be written as a…

Sum of Squares Decompositions in Hölder Spaces

Regularity of Singular Solutions to p-Poisson Equations

Regularity Preserving Sum of Squares Decompositions

Regularity of Singular Solutions to $p$ -Poisson Equations