Boundary value problems for a family of domains in the Sierpinski gasket

zbMath1323.28013arXiv1310.6463MaRDI QIDQ491467

Hua Qiu, Rachel Kogan, Robert S. Strichartz, Zi-Jian Guo

Publication date: 25 August 2015

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.6463

zbMATH Keywords

energy functionalGreen's functionharmonic functionSierpiński gasketKigami Laplacian

Mathematics Subject Classification ID

Fractals (28A80)

Related Items (9)

The average trapping time on a half Sierpinski gasket ⋮ Laplacian growth and sandpiles on the Sierpiński gasket: limit shape universality and exact solutions ⋮ Some properties of the derivatives on Sierpinski gasket type fractals ⋮ A trace theorem for Sobolev spaces on the Sierpinski gasket ⋮ Exact spectrum of the Laplacian on a domain in the Sierpinski gasket ⋮ ``The Sierpinski gasket minus its bottom line as a tree of Sierpinski gaskets ⋮ Boundary value problems on part of a level-\(n\) Sierpinski gasket ⋮ Boundary value problems for harmonic functions on domains in Sierpinski gaskets ⋮ The Dirichlet heat kernel in inner uniform domains in fractal-type spaces

Cites Work

• Extensions and their minimizations on the Sierpinski gasket
• Hausdorff measure of infinitely generated self-similar sets
• Quasiconformal mappings and extendability of functions in Sobolev spaces
• Some properties of Laplacians on fractals
• Function spaces on fractals
• Boundary value problems on a half Sierpiński gasket
• Degree-independent Sobolev extension on locally uniform domains
• Boundary value problems for harmonic functions on a domain in the Sierpinski gasket
• Conformal energy, conformal Laplacian, and energy measures on the Sierpinski gasket

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