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 Mat. Sb. (N.S.), 1987, Volume 133(175), Number 4(8), Pages 446–468 (Mi msb2619)

On boundary properties of solutions of elliptic equations in multidimensional domains representable by means of the difference of convex functions

V. Yu. Shelepov

Abstract: The author examines the solution of a linear second order uniformly elliptic equation with variable coefficients defined inside a domain whose boundary is locally representable with the aid of the difference of convex functions (the spatial analog of Radon domain without cusps in the plane). We introduce the concept of “$p$-area integral”, generalizing the known Luzin area integral. Local and integral theorems are obtained on the connection between this integral and the nontangential maximal function of the solution, and also the conditions for existence of nontangential boundary values almost everywhere and in the $L_2$-metric.
Bibliography: 17 titles.

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English version:
Mathematics of the USSR-Sbornik, 1988, 61:2, 437–460

Bibliographic databases:

UDC: 517.9
MSC: 35J25, 35J67

Citation: V. Yu. Shelepov, “On boundary properties of solutions of elliptic equations in multidimensional domains representable by means of the difference of convex functions”, Mat. Sb. (N.S.), 133(175):4(8) (1987), 446–468; Math. USSR-Sb., 61:2 (1988), 437–460

Citation in format AMSBIB
\Bibitem{She87} \by V.~Yu.~Shelepov \paper On boundary properties of solutions of elliptic equations in multidimensional domains representable by means of the difference of convex functions \jour Mat. Sb. (N.S.) \yr 1987 \vol 133(175) \issue 4(8) \pages 446--468 \mathnet{http://mi.mathnet.ru/msb2619} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=911802} \zmath{https://zbmath.org/?q=an:0686.35051|0646.35035} \transl \jour Math. USSR-Sb. \yr 1988 \vol 61 \issue 2 \pages 437--460 \crossref{https://doi.org/10.1070/SM1988v061n02ABEH003217} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1987R193700011} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84956082069} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Shelepov V., “Boundary Properties of the Solutions for Strongly Elliptic-Systems in Nonsmooth Spatial Regions”, no. 11, 1987, 21–24
2. A. K. Gushchin, “On the Dirichlet problem for a second-order elliptic equation”, Math. USSR-Sb., 65:1 (1990), 19–66
3. Shelepov V., “Boundary Properties of the Elliptic-Equations Solutions in the Nonsmooth Space Regions (Lp-Weight Case)”, no. 2, 1988, 21–24
4. Shelepov V. Tedeyev A., “On One Inequality for Elliptic Equation Solutions and its Applicability in the Theory of Boundary Properties”, 315, no. 1, 1990, 40–43
5. A. F. Tedeev, “Lokalnye svoistva reshenii zadachi Koshi dlya kvazilineinogo parabolicheskogo uravneniya vtorogo poryadka”, Vladikavk. matem. zhurn., 10:2 (2008), 46–57
6. Gushchin A.K., “Estimates of the Nontangential Maximal Function for Solutions of a Second-Order Elliptic Equation”, Dokl. Math., 86:2 (2012), 667–669
7. A. K. Guschin, “$L_p$-otsenki nekasatelnoi maksimalnoi funktsii dlya reshenii ellipticheskogo uravneniya vtorogo poryadka”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(30) (2013), 53–69
8. A. K. Gushchin, “$L_p$-estimates for the nontangential maximal function of the solution to a second-order elliptic equation”, Sb. Math., 207:10 (2016), 1384–1409
9. A. K. Gushchin, “The Luzin area integral and the nontangential maximal function for solutions to a second-order elliptic equation”, Sb. Math., 209:6 (2018), 823–839
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