## A characterization for elliptic problems on fractal sets

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- by Giovanni Molica Bisci and Vicenţiu D. Rădulescu PDF
- Proc. Amer. Math. Soc.
**143**(2015), 2959-2968 Request permission

## Abstract:

In this paper we prove a characterization theorem on the existence of one non-zero strong solution for elliptic equations defined on the Sierpiński gasket. More generally, the validity of our result can be checked studying elliptic equations defined on self-similar fractal domains whose spectral dimension $\nu \in (0,2)$. Our theorem can be viewed as an elliptic version on fractal domains of a recent contribution obtained in a recent work of Ricceri for a two-point boundary value problem.## References

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## Additional Information

**Giovanni Molica Bisci**- Affiliation: Patrimonio, Architettura e Urbanistica, Department, University of Reggio Calabria, 89124 - Reggio Calabria, Italy
- Email: gmolica@unirc.it
**Vicenţiu D. Rădulescu**- Affiliation: Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
- MR Author ID: 143765
- ORCID: 0000-0003-4615-5537
- Email: vicentiu.radulescu@math.cnrs.fr
- Received by editor(s): December 27, 2013
- Received by editor(s) in revised form: February 3, 2014, and February 9, 2014
- Published electronically: February 13, 2015
- Communicated by: Catherine Sulem
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**143**(2015), 2959-2968 - MSC (2010): Primary 35J20; Secondary 28A80, 35J25, 35J60, 47J30, 49J52
- DOI: https://doi.org/10.1090/S0002-9939-2015-12475-6
- MathSciNet review: 3336620