This article is cited in 1 paper

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.

UDC: 517.947.42

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

Received: 30.04.1976 and 30.08.1977

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

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