Inequalities for $\mathrm{BV}^{\mathbb{A}} $-Functions

TL;DR

This paper establishes new trace-type Poincaré and Sobolev inequalities for functions of bounded a-Variation, advancing the mathematical understanding of these function spaces.

Contribution

It introduces novel trace inequalities for a-a-Variation functions, extending classical results to this broader context.

Findings

Proved trace-type Poincaré inequalities

Established Sobolev inequalities for a-a-Variation functions

Extended classical inequalities to new function spaces

Abstract

In this paper, we prove trace-type Poincar\'e and Sobolev inequalities for the space of functions of bounded $\mathbb{A}$-Variation