CONVEXITY OF SOLUTIONS TO SOME ELLIPTIC PARTIAL-DIFFERENTIAL EQUATIONS

This paper is concerned with positive solutions u(x) to some special elliptic partial differential equations in a bounded convex domain OMEGA subset-of R(N). For a decreasing function g(t) the transformation v = g(u) is performed and, under appropriate restrictions on g(t), it is proved that v(x) is convex in OMEGA. Consequently, the level sets of u(x) are convex.