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Matematicheskie Zametki, 2021, Volume 109, Issue 4, Pages 552–563
DOI: https://doi.org/10.4213/mzm12468 (Mi mzm12468) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Integral Inequalities in the Theory of Hessian Operators

N. M. Ivochkina, S. I. Prokof'eva, G. V. Yakunina

St. Petersburg State University of Architecture and Civil Engineering
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DOI: https://doi.org/10.4213/mzm12468
Abstract: The paper discusses the influence of new geometric invariants of domains on Hessian integral inequalities and provides a new proof of the well-known Trudinger–Wang inequalities. A comparative analysis of the Trudinger–Wang inequalities with the classical Poincaré–Friedrichs inequality is carried out; it shows that these inequalities are qualitatively different. It is shown that Hessian integral inequalities contain information of new type and have no analogues in classical functional analysis.
Keywords: Hessian operators, Hessian integrals, Gårding cones, $p$-convex hypersurfaces.
Received: 07.06.2019
English version:
Mathematical Notes, 2021, Volume 109, Issue 4, Pages 570–579
DOI: https://doi.org/10.1134/S0001434621030251
Bibliographic databases:
Document Type: Article
UDC: 517.9+514.7+517.95+517.97
Language: Russian
Citation: N. M. Ivochkina, S. I. Prokof'eva, G. V. Yakunina, “Integral Inequalities in the Theory of Hessian Operators”, Mat. Zametki, 109:4 (2021), 552–563; Math. Notes, 109:4 (2021), 570–579
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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