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Volume 30, Issue 3
Hölder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets

D. L. Tang, R. Hu & C. W. Pan

DOI: 10.4208/ata.2014.v30.n3.6

Anal. Theory Appl., 30 (2014), pp. 296-305.

Published online: 2014-10

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  • Abstract

In this paper we establish sharp Hölder estimates of harmonic functions on a class of connected post critically finite (p.c.f.) self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some well-known examples, such as the Sierpinski gasket, the unit interval, the level $3$ Sierpinski gasket, the hexagasket, the $3$-dimensional Sierpinski gasket, and the Vicsek set are also considered.

  • Keywords

p.c.f. self-similar sets, Hölder estimates, harmonic function.

  • AMS Subject Headings

28A80

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{ATA-30-296, author = {D. L. Tang, R. Hu and C. W. Pan}, title = {Hölder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets}, journal = {Analysis in Theory and Applications}, year = {2014}, volume = {30}, number = {3}, pages = {296--305}, abstract = {

In this paper we establish sharp Hölder estimates of harmonic functions on a class of connected post critically finite (p.c.f.) self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some well-known examples, such as the Sierpinski gasket, the unit interval, the level $3$ Sierpinski gasket, the hexagasket, the $3$-dimensional Sierpinski gasket, and the Vicsek set are also considered.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2014.v30.n3.6}, url = {http://global-sci.org/intro/article_detail/ata/4494.html} }
TY - JOUR T1 - Hölder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets AU - D. L. Tang, R. Hu & C. W. Pan JO - Analysis in Theory and Applications VL - 3 SP - 296 EP - 305 PY - 2014 DA - 2014/10 SN - 30 DO - http://doi.org/10.4208/ata.2014.v30.n3.6 UR - https://global-sci.org/intro/article_detail/ata/4494.html KW - p.c.f. self-similar sets, Hölder estimates, harmonic function. AB -

In this paper we establish sharp Hölder estimates of harmonic functions on a class of connected post critically finite (p.c.f.) self-similar sets, and show that functions in the domain of Laplacian enjoy the same property. Some well-known examples, such as the Sierpinski gasket, the unit interval, the level $3$ Sierpinski gasket, the hexagasket, the $3$-dimensional Sierpinski gasket, and the Vicsek set are also considered.

D. L. Tang, R. Hu and C. W. Pan. (2014). Hölder Estimate of Harmonic Functions on a Class of p.c.f. Self-Similar Sets. Analysis in Theory and Applications. 30 (3). 296-305. doi:10.4208/ata.2014.v30.n3.6
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