Estimation of the Sobolev embedding constant on domains with minimally smooth boundary

TL;DR

This paper introduces a method to estimate the Sobolev embedding constant on domains with minimally smooth boundaries by constructing an extension operator and calculating its norm, with practical examples provided.

Contribution

The paper presents a novel approach to estimate Sobolev embedding constants on minimally smooth domains using extension operators and their norms.

Findings

Effective estimation of Sobolev embedding constants demonstrated

Extension operator construction method validated on example domains

Provides practical tools for analysis on minimally smooth domains

Abstract

In this paper, we propose a method for estimating the Sobolev type embedding constant on a domain with minimally smooth boundary. We estimate the embedding constant by constructing an extension operator and computing its operator norm. We also present some examples of estimating the embedding constant for certain domains.