This article is cited in 6 papers

A theorem on the internal derivative for a weakly degenerate second-order elliptic equation

L. I. Kamynin


Abstract: 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.

UDC: 517.9

MSC: Primary 35J70; Secondary 35B50

Received: 06.12.1983

 English version: Mathematics of the USSR-Sbornik, 1986, 54:2, 297–316

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