Geodesic
A~theorem on the internal derivative for a~weakly degenerate second-order elliptic equation
Sbornik. Mathematics, Tome 54 (1986) no. 2, pp. 297-316

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For a second-order elliptic equation admitting a weak degeneracy near the boundary, conditions on the geometry of the boundary and on the order of the degeneracy of the equation are given under which every neighborhood of a boundary point where a solution attains an extremum contains a boundary point where the derivative of the solution in an internal direction is necessarily different from zero. Bibliography: 12 titles. 
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     author = {L. I. Kamynin},
     title = {A~theorem on the internal derivative for a~weakly degenerate second-order elliptic equation},
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     volume = {54},
     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/SM_1986_54_2_a1/}
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L. I. Kamynin. A~theorem on the internal derivative for a~weakly degenerate second-order elliptic equation. Sbornik. Mathematics, Tome 54 (1986) no. 2, pp. 297-316. http://geodesic.mathdoc.fr/item/SM_1986_54_2_a1/