Abstract:
We discuss the relations between two types of fractional Laplacians
– “Dirichlet” and “Navier” ones – in bounded domains in $\mathbb R^n$.
Then we prove the coincidence of the Sobolev and Hardy constants relative
to these operators of any real order $m\in(0,\frac{n}{2})$.
This talk is based on joint papers with Roberta Musina, see [1], [2], [3].
Author was supported by RFBR grant 14-01-00534 and by St.-Petersburg University grant 6.38.670.2013.
Supplementary materials:
abstract.pdf (79.8 Kb)
Language: English
References
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R. Musina, A. I. Nazarov, “On fractional Laplacians”, Comm. in PDEs, 39:9 (2014), 1780–1790
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R. Musina, A. I. Nazarov, On fractional Laplacians–2, 2014, arXiv: 1408.3568
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R. Musina, A. I. Nazarov, “On the Sobolev and Hardy constants for the fractional Navier Laplacian”, Nonlinear Analysis, 121 (2015), 123–129
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