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Mat. Tr., 2014, Volume 17, Number 1, Pages 175–201 (Mi mt272)  

This article is cited in 1 scientific paper (total in 1 paper)

Discrete Hölder estimates for a parametrix variation

A. I. Parfenov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: In nonhomogeneous Hölder spaces, we prove continuity of integral operators with kernels from a special class and indicate simplest properties of this class. A parametrix of new type is constructed in a half-space for second order elliptic operators. We establish that, in local Hölder norms, it admits more exact estimate than that for a parametrix close to the Levi function.

Key words: Hölder space, integral operator, parametrix, discretization, stability of the Green functions.

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English version:
Siberian Advances in Mathematics, 2015, 25:3, 209–229

Bibliographic databases:

Document Type: Article
UDC: 517.518.1
Received: 07.06.2013

Citation: A. I. Parfenov, “Discrete Hölder estimates for a parametrix variation”, Mat. Tr., 17:1 (2014), 175–201; Siberian Adv. Math., 25:3 (2015), 209–229

Citation in format AMSBIB
\Bibitem{Par14}
\by A.~I.~Parfenov
\paper Discrete H\"older estimates for a~parametrix variation
\jour Mat. Tr.
\yr 2014
\vol 17
\issue 1
\pages 175--201
\mathnet{http://mi.mathnet.ru/mt272}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3236366}
\transl
\jour Siberian Adv. Math.
\yr 2015
\vol 25
\issue 3
\pages 209--229
\crossref{https://doi.org/10.3103/S1055134415030062}


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    This publication is cited in the following articles:
    1. A. I. Parfenov, “Dicrete Hölder estimates for a certain kind of parametrix. II”, Ufa Math. J., 9:2 (2017), 62–91  mathnet  crossref  isi  elib
  • Математические труды Siberian Advances in Mathematics
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