On estimate for the modulus of continuity of the Cauchy-type integral having a Lipschitz-continuous density

✍ Scribed by Jaroslav Drobek

• Book ID: 119932466
• Publisher: SP Versita
• Year: 2013
• Tongue: English
• Weight: 325 KB
• Volume: 63
• Category: Article
• ISSN: 0139-9918
• DOI: 10.2478/s12175-012-0085-y

✦ Synopsis

Abstract

The Cauchy-type integral having a Lipschitz-continuous density is under investigation. It is considered in a Jordan region that has a piecewise regular boundary without cusps and therefore it can be continuously extended over the closure of the region. Then the boundary values form a function, whose modulus of continuity is to be estimated. One parameter-dependent estimate is obtained and one algorithm for its evaluating is developed. The algorithm is demonstrated on some examples.