ON THE BEHAVIOR AT INFINITY OF SOLUTIONS OF SECOND ORDER ELLIPTIC EQUATIONS IN DOMAINS WITH NONCOMPACT BOUNDARY
O A Oleĭnik, G A Iosif'jan · Mathematics of the USSR-Sbornik · 1981
In this paper the behavior at infinity of solutions of second order elliptic equations is studied. Here the solutions satisfy homogeneous Dirichlet conditions, Neumann conditions or periodicity conditions, in each case on the part of the boundary that belongs to some neighborhood of infinity. The authors obtain a priori estimates characterizing the behavior, as , of these solutions in domains with noncompact boundary, depending on the geometric properties of the domain and the behavior, again as , of the function on the right side of the equation. Bibliography: 13 titles.