Convexity of level sets for solutions to nonlinear elliptic problems in convex rings
Texas State University-San Marcos, Department of Mathematics
We find suitable assumptions for the quasi-concave envelope u* of a solution (or a subsolution) u of an elliptic equation F(x, u, ∇u, D2u) = 0 (possibly fully nonlinear) to be a viscosity subsolution of the same equation. We apply this result to study the convexity of level sets of solutions to elliptic Dirichlet problems in a convex ring Ω = Ω0 \ Ω‾1.
Elliptic equations, Convexity of level sets, Quasi-concave envelope
Cuoghi, P., & Salani, P. (2006). Convexity of level sets for solutions to nonlinear elliptic problems in convex rings. <i>Electronic Journal of Differential Equations, 2006</i>(124), pp. 1-12.