Abstract
We investigate the convexity of level sets of solutions to general elliptic equations in a convex ring Ω. In particular, if u is a classical solution which has constant (distinct) values on the two connected components of ∂Ω, we consider its quasi-concave envelope u* (i.e., the function whose superlevel sets are the convex envelopes of those of u) and we find suitable assumptions which force u * to be a subsolution of the equation. If a comparison principle holds, this yields u = u* and then u is quasi-concave.
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