Criteria for $C^1$-approximability of functions on compact sets in ${\mathbb{R}}^N$, $N \geq 3$, by solutions of second-order homogeneous elliptic equations
- Authors: Paramonov P.V.1,2
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Affiliations:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Saint Petersburg State University
- Issue: Vol 85, No 3 (2021)
- Pages: 154-177
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133861
- DOI: https://doi.org/10.4213/im9036
- ID: 133861
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Abstract
We obtain capacitive criteria for the approximability of individual functions by solutions of second-order homogeneous ellipticequations with constant complex coefficients in the norm of a Whitney-type $C^1$-space on a compact setin $\mathbb{R}^N$, $N \geq 3$. The case $N=2$ was studied in a recent paper by the author and Tolsa.For $C^1$-approximations by harmonic functions (with any $N$), weaker criteria were earlier found by the author.We establish some metric properties of the capacities considered.
About the authors
Petr Vladimirovich Paramonov
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Saint Petersburg State University
Email: petr.paramonov@list.ru
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