On Trace Theorems and Poincare inequality for one-dimensional Sobolev spaces

TL;DR

This paper discusses trace theorems and Poincare inequalities specifically for one-dimensional Sobolev spaces, providing foundational results relevant to analysis on intervals.

Contribution

It introduces versions of trace theorems and Poincare inequalities tailored for one-dimensional Sobolev spaces, extending classical results to this setting.

Findings

Established trace theorems for Sobolev spaces on intervals

Derived a one-dimensional Poincare inequality

Provided foundational tools for analysis in one-dimensional Sobolev spaces

Abstract

In these notes, we present versions of trace theorems for Sobolev spaces over an interval in the real line, and also a one-dimensional version of the well-known Poincare inequality.