2013/10/24 by Zijian Guo, Guo, Zijian, Hua Qiu +3
Mathematics · #28A80 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #advanced mathematical theories #math.CA #math.FA #msc:28A80
paper · pdf · doi:10.48550/arxiv.1310.6463
19pages, 10 figures
arxiv created 2013/10/24 · openalex publication_date 2013/10/24 · arxiv updated 2013/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a family of domains in the Sierpinski gasket, we study harmonic functions of finite energy, characterizing them in terms of their boundary values, and study their normal derivatives on the boundary. We characterize those domains for which there is an extension operator for functions of finite energy. We give an explicit construction of the Green's function for these domains.