D. Azagra

activity

20002024

most citedGlobal and fine approximation of convex functions

35 citations · 60 across the 35 of their papers we have counts for

collaborators

44 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.CA2023★ 1 cited

$C^{2}$ -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…

math.CA2023

A geometric approach to second-order differentiability of convex functions

Daniel Azagra, Anthony Cappello, Piotr Hajłasz

We show a new, elementary and geometric proof of the classical Alexandrov theorem about the second order differentiability of convex functions. We also show new proofs of recent re…

math.MG2022

Inner and outer smooth approximation of convex hypersurfaces. When is it possible?

Daniel Azagra, Dmitriy Stolyarov

Let $S$ be a convex hypersurface (the boundary of a closed convex set $V$ with nonempty interior) in $R^{n}$ . We prove that $S$ contains no lines if and only if for every op…

math.CA2020

Lusin-type properties of convex functions and convex bodies

Daniel Azagra, Piotr Hajłasz

We prove that if $f : R^{n} \to R$ is convex and $A \subset R^{n}$ has finite measure, then for any $ε > 0$ there is a convex function $g:\mathbb{R}^n\to\m…

math.FA2019

$C^{1, ω}$ extension formulas for $1$ -jets on Hilbert spaces

Daniel Azagra, Carlos Mudarra

We provide necessary and sufficient conditions for a $1$ -jet $(f, G) : E \to R \times X$ to admit an extension $(F, \nabla F)$ for some $F \in C^{1, ω} (X)$ . Here $E$ s…