This article is cited in 7 papers

On an approach to the study of qualitative properties of solutions of nondivergence elliptic equations of second order

A. A. Novruzov


Abstract: The author studies some important interior and boundary properties of solutions of linear and quasilinear second order elliptic equations, which may in general be degenerate on the boundary of a (bounded or unbounded) domain. An a priori estimate of the Hölder norm of the solution is obtained, and new theorems are proved on regularity of a boundary point with respect to the Dirichlet problem. The Harnack inequality and Phragmén–Lindelöf type theorems are also proved.
Bibliography: 37 titles.

UDC: 517.944

MSC: Primary 35J25, 35J67, 35B45; Secondary 35J70

Received: 28.09.1982

 English version: Mathematics of the USSR-Sbornik, 1985, 50:2, 343–367

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