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 Mat. Sb. (N.S.), 1978, Volume 106(148), Number 2(6), Pages 162–182 (Mi msb2564)

On local estimates near the boundary of solutions of a second order equation with nonnegative characteristic form

L. I. Kamynin, B. N. Khimchenko

Abstract: Using barrier functions the authors study the connection between the geometric configuration of a domain, the order of degeneracy of the highest coefficients of an equation (near the boundary) and the behavior of solutions of these equations near the boundary of the domain of continuity of the solutions. The results obtained can be applied first to study local regularity of solutions near the boundary and secondly to theorems of Giraud type on the sign of the oblique derivative at boundary points when the solution attains its extremal values.
Bibliography: 10 titles.

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English version:
Mathematics of the USSR-Sbornik, 1978, 34:6, 715–735

Bibliographic databases:

UDC: 517.947.42
MSC: Primary 35M05; Secondary 35J70, 35K20

Citation: L. I. Kamynin, B. N. Khimchenko, “On local estimates near the boundary of solutions of a second order equation with nonnegative characteristic form”, Mat. Sb. (N.S.), 106(148):2(6) (1978), 162–182; Math. USSR-Sb., 34:6 (1978), 715–735

Citation in format AMSBIB
\Bibitem{KamKhi78} \by L.~I.~Kamynin, B.~N.~Khimchenko \paper On local estimates near the boundary of solutions of a~second order equation with nonnegative characteristic form \jour Mat. Sb. (N.S.) \yr 1978 \vol 106(148) \issue 2(6) \pages 162--182 \mathnet{http://mi.mathnet.ru/msb2564} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=503591} \zmath{https://zbmath.org/?q=an:0385.35007|0414.35013} \transl \jour Math. USSR-Sb. \yr 1978 \vol 34 \issue 6 \pages 715--735 \crossref{https://doi.org/10.1070/SM1978v034n06ABEH001344} 

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This publication is cited in the following articles:
1. Kamynin L., Khimchenko B., “Theorems Concerning the Sign of the Derivative for a 2nd-Order Elliptic Equation”, Differ. Equ., 20:4 (1984), 485–494
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