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Funktsional'nyi Analiz i ego Prilozheniya, 2020, Volume 54, Issue 4, Pages 85–97
DOI: https://doi.org/10.4213/faa3828
(Mi faa3828)
 

This article is cited in 4 scientific papers (total in 4 papers)

On the Constancy of the Extremal Function in the Embedding Theorem of Fractional Order

N. S. Ustinov

Saint Petersburg State University, St. Petersburg, Russia
Full-text PDF (569 kB) Citations (4)
References:
Abstract: We consider the problem of the constancy of the minimizer in the fractional embedding theorem $\mathcal{H}^s(\Omega) \hookrightarrow L_q(\Omega)$ for a bounded Lipschitz domain $\Omega$, depending on the domain size. For the family of domains $\varepsilon \Omega$, we prove that, for small dilation coefficients $\varepsilon$, the unique minimizer is constant, whereas for large $\varepsilon$, a constant function is not even a local minimizer. We also discuss whether a constant function is a global minimizer if it is a local one.
Keywords: fractional Laplace operators, constancy of the minimizer, spectral Dirichlet Laplacian.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00630
Received: 12.08.2020
Revised: 12.08.2020
Accepted: 23.08.2020
English version:
Functional Analysis and Its Applications, 2020, Volume 54, Issue 4, Pages 295–305
DOI: https://doi.org/10.1134/S0016266320040073
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: N. S. Ustinov, “On the Constancy of the Extremal Function in the Embedding Theorem of Fractional Order”, Funktsional. Anal. i Prilozhen., 54:4 (2020), 85–97; Funct. Anal. Appl., 54:4 (2020), 295–305
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/faa3828
  • https://doi.org/10.4213/faa3828
  • https://www.mathnet.ru/eng/faa/v54/i4/p85
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Функциональный анализ и его приложения Functional Analysis and Its Applications
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    References:79
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