Regularity of solutions to the polyharmonic equation in general domains

• 成果类型: Article
• 署名作者: Mayboroda, Svitlana; Maz'ya, Vladimir
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; University of Liverpool; Linkoping University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0464-1
• 发表日期: 2014
• 页码: 1-68
• 关键词: p dirichlet problem; biharmonic functions; green-function; elliptic-systems; Neumann problem; wiener test; lipschitz; BOUNDARY

摘要

The present paper establishes boundedness of derivatives for the solutions to the polyharmonic equation of order 2m in arbitrary bounded open sets of , 2a parts per thousand currency signna parts per thousand currency sign2m+1, without any restrictions on the geometry of the underlying domain. It is shown that this result is sharp and cannot be improved in general domains. Moreover, it is accompanied by sharp estimates on the polyharmonic Green function.