Semilinear elliptic equations in convex domains and convex rings


François Hamel

10:10:00 - 11:00:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, I will discuss some geometrical properties of positive solutions of some semilinear elliptic equations in bounded convex domains or convex rings, with Dirichlet-type boundary conditions. A solution is called quasiconcave if its superlevel sets are convex. I will present two counterexamples, that is two cases of semilinear elliptic equations for which the solutions are not quasiconcave. This talk is based on a joint work with N. Nadirashvili and Y. Sire.

For material related to this talk, click here.