On $\gamma _{\mathcal {L}}$-capacities of Cantor sets
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M. Ya. Mazalov;
Translated by: S. V. Kislyakov - St. Petersburg Math. J. 35 (2024), 869-877
- DOI: https://doi.org/10.1090/spmj/1833
- Published electronically: December 3, 2024
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Abstract:
Let $\mathcal {C}$ be a homogeneous elliptic second-order differential operator in $\mathbb {R}^d$, $d\ge 3$, with constant complex coefficients. In terms of the capacities $\gamma _{\mathcal {C}}$, the removable singularities of $\mathrm {L} ^{\infty }$-bounded solutions of the equations $\mathcal {C} f=0$ are described. For Cantor sets in $\mathbb {R}^d$ it is shown that $\gamma _{\mathcal {C}}$ is comparable with classical harmonic capacities of the potential theory for all $\mathcal {C}$ and corresponding $d$.References
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Bibliographic Information
- M. Ya. Mazalov
- Affiliation: National research university “Moscow Power Engineering Institute”, Branch in Smolensk, Energeticheskii proezd, 1, Smolensk, Russia; St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, Russia
- Email: maksimmazalov@yandex.ru
- Received by editor(s): March 27, 2023
- Published electronically: December 3, 2024
- Additional Notes: This work was done under support of the Russian Science Foundation (grant 22-11-00071).
- © Copyright 2024 American Mathematical Society
- Journal: St. Petersburg Math. J. 35 (2024), 869-877
- MSC (2020): Primary 31B15
- DOI: https://doi.org/10.1090/spmj/1833