Quasiconcave solutions to elliptic problems in convex rings Chiara BianchiniMarco LonginettiPaolo Salani 35J2535J6535B05convexitylevel setselliptic equationsquasiconcave envelopeMinkowski addition We investigate the convexity of level sets of solutions to general elliptic equations in a convex ring $\Omega$. In particular, if $u$ is a classical solution which has constant (distinct) values on the two connected components of $\partial\Omega$, 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. Indiana University Mathematics Journal 2009 text pdf 10.1512/iumj.2009.58.3539 10.1512/iumj.2009.58.3539 en Indiana Univ. Math. J. 58 (2009) 1565 - 1590 state-of-the-art mathematics http://iumj.org/access/