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Geometry of solutions for semi-linear equations in convex domains Sire, Yannick


It was believed for a long time by the community that solutions of semi linear equations with reasonable nonlinearities in convex domains would be quasi-concave (i.e. their super level sets would be convex). We provide a counter-example to this conjecture in the plane. This is joint work with F. Hamel and N. Nadirashvili.

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