Abstract

This paper deals with some geometrical properties of solutions of some semilinear elliptic equations in bounded convex domains or convex rings. Constant boundary conditions are imposed on the single component of the boundary when the domain is convex, or on each of the two components of the boundary when the domain is a convex ring. A function is called quasiconcave if its superlevel sets, defined in a suitable way when the domain is a convex ring, are all convex. In this paper, we prove that the superlevel sets of the solutions do not always inherit the convexity or ring-convexity of the domain. Namely, we give two counterexamples to this quasiconcavity property: the first one for some two-dimensional convex domains and the second one for some convex rings in any dimension.

pdf

Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 499-527
Launched on MUSE
2016-04-04
Open Access
No
Back To Top

This website uses cookies to ensure you get the best experience on our website. Without cookies your experience may not be seamless.