Geodesic
On local estimates near the boundary of solutions of a~second order equation with nonnegative characteristic form
Sbornik. Mathematics, Tome 34 (1978) no. 6, pp. 715-735

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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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     author = {L. I. Kamynin and B. N. Khimchenko},
     title = {On local estimates near the boundary of solutions of a~second order equation with nonnegative characteristic form},
     journal = {Sbornik. Mathematics},
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     volume = {34},
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     year = {1978},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1978_34_6_a2/}
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L. I. Kamynin; B. N. Khimchenko. On local estimates near the boundary of solutions of a~second order equation with nonnegative characteristic form. Sbornik. Mathematics, Tome 34 (1978) no. 6, pp. 715-735. http://geodesic.mathdoc.fr/item/SM_1978_34_6_a2/