Acker, Andrew; Poghosyan, Michael; Shahgholian, Henrik
(Taylor & Francis Group, LLC, 2006-05)

For a given convex ring and an L 1 function f:Ω × → + we show, under suitable assumptions on f, that there exists a solution (in the weak sense) to
with {x Ω: u(x) > s} Ω1 convex, for all s (0, M).