Marjorie K. Drake

collaborators

4 papers

math.CA2024

$C^{2}$ -Lusin approximation of strongly convex bodies

Daniel Azagra, Marjorie Drake, Piotr Hajłasz

We prove that, if $W \subset R^{n}$ is a locally strongly convex body (not necessarily compact), then for any open set $V \supset \partial W$ and $ε > 0$ , and $V \su…

math.CA2024

Sobolev extension in a simple case

Marjorie Drake, Charles Fefferman, Kevin Ren +1

In this paper, we establish the existence of a bounded, linear extension operator $T : L^{2, p} (E) \to L^{2, p} (R^{2})$ when $1 < p < 2$ and $E$ is a finite subset of $\mathbb{R}^2…

math.CA2024

Finiteness Principles for Smooth Convex Functions

Marjorie K. Drake

Let $E \subset R^{n}$ be a compact set, and $f : E \to R$ . How can we tell if there exists a convex extension $F \in C^{1, 1} (R^{n})$ of $f$ , i.e. satisfying $F…

math.CA2023

$C^{2}$ -Lusin approximation of strongly convex functions

Daniel Azagra, Marjorie Drake, Piotr Hajłasz

We prove that if $u : R^{n} \to R$ is strongly convex, then for every $ε > 0$ there is a strongly convex function $v \in C^{2} (R^{n})$ such that $|\{u\neq v…

C2-Lusin approximation of strongly convex bodies

Sobolev extension in a simple case

Finiteness Principles for Smooth Convex Functions

C2-Lusin approximation of strongly convex functions

$C^{2}$ -Lusin approximation of strongly convex bodies

$C^{2}$ -Lusin approximation of strongly convex functions