Ilmanen's Lemma on Insertion of C$^{1,1}$ Functions

TL;DR

This paper provides a proof of Ilmanen's lemma, demonstrating that a C^{1,1} function can be constructed between a locally semi-convex and a locally semi-concave function, advancing understanding of function regularity.

Contribution

The paper offers a new proof of Ilmanen's lemma, establishing the existence of C^{1,1} functions between semi-convex and semi-concave functions.

Findings

Proof of Ilmanen's lemma provided

Existence of C^{1,1} functions between semi-convex and semi-concave functions confirmed

Advances regularity results in analysis

Abstract

We give a proof of Ilmanen's lemma, which asserts that between a locally semi-convex and a locally semi-concave function it is possible to find a C$^{1,1}$ function.